Rhonda numbers

From Rosetta Code
Task
Rhonda numbers
You are encouraged to solve this task according to the task description, using any language you may know.

A positive integer n is said to be a Rhonda number to base b if the product of the base b digits of n is equal to b times the sum of n's prime factors.


These numbers were named by Kevin Brown after an acquaintance of his whose residence number was 25662, a member of the base 10 numbers with this property.


25662 is a Rhonda number to base-10. The prime factorization is 2 × 3 × 7 × 13 × 47; the product of its base-10 digits is equal to the base times the sum of its prime factors:

2 × 5 × 6 × 6 × 2 = 720 = 10 × (2 + 3 + 7 + 13 + 47)

Rhonda numbers only exist in bases that are not a prime.

Rhonda numbers to base 10 always contain at least 1 digit 5 and always contain at least 1 even digit.


Task
  • For the non-prime bases b from 2 through 16 , find and display here, on this page, at least the first 10 Rhonda numbers to base b. Display the found numbers at least in base 10.


Stretch
  • Extend out to base 36.


See also



ALGOL 68

BEGIN # find some Rhonda numbers: numbers n in base b such that the product  #
      # of the digits of n is b * the sum of the prime factors of n          #

    # returns the sum of the prime factors of n                              #
    PROC factor sum = ( INT n )INT:
         BEGIN
             INT result := 0;
             INT v      := ABS n;
             WHILE v > 1 AND v MOD 2 = 0 DO
                 result +:= 2;
                 v   OVERAB 2
             OD;
             FOR f FROM 3 BY 2 WHILE v > 1 DO
                 WHILE v > 1 AND v MOD f = 0 DO
                     result +:= f;
                     v   OVERAB f
                 OD
             OD;
             result
         END # factor sum # ;
    # returns the digit product of n in the specified base                   #
    PROC digit product = ( INT n, base )INT:
         IF n = 0 THEN 0
         ELSE
             INT result := 1;
             INT v      := ABS n;
             WHILE v > 0 DO
                 result *:= v MOD base;
                 v   OVERAB base
             OD;
             result
         FI # digit product # ;
    # returns TRUE  if n is a Rhonda number in the specified base,           #
    #         FALSE otherwise                                                #
    PROC is rhonda = ( INT n, base )BOOL: base * factor sum( n ) = digit product( n, base );

    # returns TRUE if n is prime, FALSE otherwise                            #
    PROC is prime = ( INT n )BOOL:
         IF   n < 3       THEN n = 2
         ELIF n MOD 3 = 0 THEN n = 3
         ELIF NOT ODD n   THEN FALSE
         ELSE
             INT  f          := 5;
             INT  f2         := 25;
             INT  to next    := 24;
             BOOL is a prime := TRUE;
             WHILE f2 <= n AND is a prime DO
                 is a prime := n MOD f /= 0;
                 f         +:= 2;
                 f2        +:= to next;
                 to next   +:= 8
             OD;
             is a prime
         FI # is prime # ;
    # returns a string representation of n in the specified base             #
    PROC to base string = ( INT n, base )STRING:
         IF n = 0 THEN "0"
         ELSE
             INT under 10 = ABS "0";
             INT over 9   = ABS "a" - 10;
             STRING result := "";
             INT    v      := ABS n;
             WHILE v > 0 DO
                 INT d = v MOD base;
                 REPR ( d + IF d < 10 THEN under 10 ELSE over 9 FI ) +=: result;
                 v OVERAB base
             OD;
             result
         FI # to base string # ;
    # find the first few Rhonda numbers in non-prime bases 2 .. max base     #
    INT max rhonda = 10;
    INT max base   = 16;
    FOR base FROM 2 TO max base DO
        IF NOT is prime( base ) THEN
            print( ( "The first ", whole( max rhonda, 0 )
                   , " Rhonda numbers in base ", whole( base, 0 )
                   , ":", newline
                   )
                 );
            INT r count := 0;
            [ 1 : max rhonda ]INT rhonda;
            FOR n WHILE r count < max rhonda DO
                IF is rhonda( n, base ) THEN
                    rhonda[ r count +:= 1 ] := n
                FI
            OD;
            print( ( "    in base 10:" ) );
            FOR i TO max rhonda DO print( ( " ", whole( rhonda[ i ], 0 ) ) ) OD;
            print( ( newline ) );
            IF base /= 10 THEN
                print( ( "    in base ", whole( base, -2 ), ":" ) );
                FOR i TO max rhonda DO print( ( " ", to base string( rhonda[ i ], base ) ) ) OD;
                print( ( newline ) )
            FI
        FI
    OD
END
Output:
The first 10 Rhonda numbers in base 4:
    in base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713
    in base  4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221
The first 10 Rhonda numbers in base 6:
    in base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992
    in base  6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132
The first 10 Rhonda numbers in base 8:
    in base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956
    in base  8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544
The first 10 Rhonda numbers in base 9:
    in base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857
    in base  9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376
The first 10 Rhonda numbers in base 10:
    in base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
The first 10 Rhonda numbers in base 12:
    in base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849
    in base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35
The first 10 Rhonda numbers in base 14:
    in base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945
    in base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437
The first 10 Rhonda numbers in base 15:
    in base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758
    in base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8
The first 10 Rhonda numbers in base 16:
    in base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070
    in base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e

Arturo

digs: (@`0`..`9`) ++ @`A`..`Z`
toBase: function [n,base][
    join map digits.base:base n 'x -> digs\[x]
]

rhonda?: function [n,base][
    (base * sum factors.prime n) = product digits.base:base n
]

nonPrime: select 2..16 'x -> not? prime? x

loop nonPrime 'npbase [
    print "The first 10 Rhonda numbers, base-" ++ (to :string npbase) ++ ":"
    rhondas: select.first:10 1..∞ 'z -> rhonda? z npbase
    print ["In base 10 ->" join.with:", " to [:string] rhondas]
    print ["In base" npbase "->" join.with:", " to [:string] map rhondas 'w -> toBase w npbase]
    print ""
]
Output:
The first 10 Rhonda numbers, base-4:
In base 10 -> 10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713 
In base 4 -> 2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221 

The first 10 Rhonda numbers, base-6:
In base 10 -> 855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992 
In base 6 -> 3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132 

The first 10 Rhonda numbers, base-8:
In base 10 -> 1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956 
In base 8 -> 3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544 

The first 10 Rhonda numbers, base-9:
In base 10 -> 15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857 
In base 9 -> 23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376 

The first 10 Rhonda numbers, base-10:
In base 10 -> 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985 
In base 10 -> 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985 

The first 10 Rhonda numbers, base-12:
In base 10 -> 560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849 
In base 12 -> 3A8, 568, 2389, 2689, 27B6, 29B4, 4297, 4974, 5483, 6A35 

The first 10 Rhonda numbers, base-14:
In base 10 -> 11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945 
In base 14 -> 4279, 6B27, 76CD, AB27, B7C1, 1277D, 173DA, 17547, 17BC2, 19437 

The first 10 Rhonda numbers, base-15:
In base 10 -> 2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758 
In base 15 -> A97, AEC, 35E8, 4A83, 5269, 5586, 5A1C, 5E39, 735D, 91A8 

The first 10 Rhonda numbers, base-16:
In base 10 -> 1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070 
In base 16 -> 3E8, 46E, 1A78, 3E28, 4CA8, 4E4B, 4F83, 5D8A, 66B8, 718E

C++

#include <algorithm>
#include <cassert>
#include <iomanip>
#include <iostream>

int digit_product(int base, int n) {
    int product = 1;
    for (; n != 0; n /= base)
        product *= n % base;
    return product;
}

int prime_factor_sum(int n) {
    int sum = 0;
    for (; (n & 1) == 0; n >>= 1)
        sum += 2;
    for (int p = 3; p * p <= n; p += 2)
        for (; n % p == 0; n /= p)
            sum += p;
    if (n > 1)
        sum += n;
    return sum;
}

bool is_prime(int n) {
    if (n < 2)
        return false;
    if (n % 2 == 0)
        return n == 2;
    if (n % 3 == 0)
        return n == 3;
    for (int p = 5; p * p <= n; p += 4) {
        if (n % p == 0)
            return false;
        p += 2;
        if (n % p == 0)
            return false;
    }
    return true;
}

bool is_rhonda(int base, int n) {
    return digit_product(base, n) == base * prime_factor_sum(n);
}

std::string to_string(int base, int n) {
    assert(base <= 36);
    static constexpr char digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    std::string str;
    for (; n != 0; n /= base)
        str += digits[n % base];
    std::reverse(str.begin(), str.end());
    return str;
}

int main() {
    const int limit = 15;
    for (int base = 2; base <= 36; ++base) {
        if (is_prime(base))
            continue;
        std::cout << "First " << limit << " Rhonda numbers to base " << base
                  << ":\n";
        int numbers[limit];
        for (int n = 1, count = 0; count < limit; ++n) {
            if (is_rhonda(base, n))
                numbers[count++] = n;
        }
        std::cout << "In base 10:";
        for (int i = 0; i < limit; ++i)
            std::cout << ' ' << numbers[i];
        std::cout << "\nIn base " << base << ':';
        for (int i = 0; i < limit; ++i)
            std::cout << ' ' << to_string(base, numbers[i]);
        std::cout << "\n\n";
    }
}
Output:
First 15 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12: 3A8 568 2389 2689 27B6 29B4 4297 4974 5483 6A35 6B64 7662 86B8 8864 94B4

First 15 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14: 4279 6B27 76CD AB27 B7C1 1277D 173DA 17547 17BC2 19437 1A873 1B17A 25377 28427 33A75

First 15 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15: A97 AEC 35E8 4A83 5269 5586 5A1C 5E39 735D 91A8 936A 9BA4 9E1A B385 BA73

First 15 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16: 3E8 46E 1A78 3E28 4CA8 4E4B 4F83 5D8A 66B8 718E 7CA2 7E24 85BC 86D9 8E71

First 15 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18: 49C 94C 1998 2G9F 35FG 39D4 3B36 3E6G 49F8 64E9 6A6E 77A9 7G19 8696 956D

First 15 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20: 4AF 17CA 1I4F 2CI5 2F85 3GF2 465A 46C5 55EC 5A85 6A2J 6DAG 84H5 9G1A A1FC

First 15 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21: 3EF C4E J67 189E 1EBC 2EG6 33EC 3E2I 45E9 55I7 5697 6D3E 93J7 9E34 9J37

First 15 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22: 5CB 8BE G5B 2FB2 2LB8 3AB4 6GB1 6LBC B16G B1CJ B96A BI78 C7BL G9FB I25B

First 15 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24: 3EG 4GL 6LG 9IC 9JG C9G E9G FG6 HCE 16DK 1BGF 1IHG 1LCG 22CI 26EI

First 15 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25: AKE FA8 L5A 1A5M 3AA7 3H5F 45FF 4AA6 655E 8O55 93F5 95JA A5DO AA2F AEK4

First 15 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26: BDE DKE DME GD6 16KD 1F6D 1PGD 2E6D 2I2D 2KMD 3ECD 43ED 45KD 64MD 7DIE

First 15 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27: 6FI G6I GF9 I2O K9I O9B 169K 19NI 1AII 29JF 2I9J 2Q9I 32IG 337L 339L

First 15 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28: 3QE 7BC 7C8 9EE E6G HC7 16LQ 17QQ 18EM 1M67 1MCE 273O 28OE 2AL6 2BEI

First 15 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30: 3AO 3FI 5KF 5S6 6IA 7FC 8IA 8P6 9CA AFQ AJ6 AS9 BFA CN5 EEF

First 15 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32: 1SO 3GG D6G FG4 GAS GEH OQ2 P4O S8N 1EBG 1GEA 1HOO 1S4S 1VC8 288L

First 15 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33: MU 6FB 6VB CMW MTF S3M 1LGB 1PBU 1Q3M 3LML 6B78 7BFB 8O2B 9BTG 9JM8

First 15 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34: 4UH C8H DHE E8H J6H W4H 36LH 3EHI 3F4H 3HQO 3JEH 4H6E 6CSH 6H28 7HOI

First 15 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35: 6P7 7PQ 7U8 F7E P9E Y7A 17LU 17SA 1BFE 1FL7 1FPL 1J5E 2A7F 2DEF 2EBK

First 15 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36: RS 3PC 4DI 6BI 8HI 9KS A9G C5I CZ9 HRC 13TO 14OU 1G9S 1IQ9 1LW6

Factor

Works with: Factor version 0.99 2022-04-03
USING: formatting grouping io kernel lists lists.lazy math
math.parser math.primes math.primes.factors prettyprint ranges
sequences sequences.extras ;

: rhonda? ( n base -- ? )
    [ [ >base 1 group ] keep '[ _ base> ] map-product ]
    [ swap factors sum * ] 2bi = ;

: rhonda ( base -- list ) 1 lfrom swap '[ _ rhonda? ] lfilter ;

: list. ( list base -- ) '[ _ >base write bl ] leach nl ;

:: rhonda. ( base -- )
    15 base rhonda ltake :> r
    base "First 15 Rhonda numbers to base %d:\n" printf
    "In base 10: " write r 10 list.
    base "In base %d: " printf r base list. ;

2 36 [a..b] [ prime? not ] filter [ rhonda. nl ] each
Output:
First 15 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902 
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232 

First 15 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821 
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553 

First 15 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429 
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345 

First 15 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944 
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316 

First 15 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662 

First 15 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264 
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4 

First 15 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543 
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75 

First 15 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483 
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73 

First 15 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465 
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71 

First 15 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229 
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d 

First 15 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712 
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc 

First 15 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798 
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37 

First 15 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753 
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b 

First 15 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458 
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei 

First 15 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504 
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4 

First 15 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302 
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die 

First 15 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500 
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l 

First 15 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938 
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei 

First 15 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035 
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef 

First 15 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005 
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l 

First 15 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858 
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8 

First 15 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614 
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi 

First 15 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305 
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk 

First 15 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030 
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6 

FreeBASIC

Translation of: ALGOL 68
'#include "isprime.bas"

Function FactorSum(n As Uinteger) As Uinteger
    Dim As Uinteger result = 0
    Dim As Uinteger v = Abs(n)
    While v > 1 And v Mod 2 = 0
        result += 2
        v \= 2
    Wend
    For f As Uinteger = 3 To v Step 2
        While v > 1 And v Mod f = 0
            result += f
            v \= f
        Wend
    Next f
    Return result
End Function

Function DigitProduct(n As Uinteger, base_ As Uinteger) As Uinteger
    If n = 0 Then Return 0
    Dim As Uinteger result = 1
    Dim As Uinteger v = Abs(n)
    While v > 0
        result *= v Mod base_
        v \= base_
    Wend
    Return result
End Function

Function isRhonda(n As Uinteger, base_ As Uinteger) As Uinteger
    Return base_ * FactorSum(n) = DigitProduct(n, base_)
End Function

Function ToBaseString(n As Uinteger, base_ As Uinteger) As String
    If n = 0 Then Return "0"
    Dim As Uinteger under10 = Asc("0")
    Dim As Uinteger over9 = Asc("a") - 10
    Dim As String result = ""
    Dim As Uinteger v = Abs(n)
    While v > 0
        Dim As Uinteger d = v Mod base_
        result = Chr(d + Iif(d < 10, under10, over9)) + result
        v \= base_
    Wend
    Return result
End Function

Dim As Uinteger maxRhonda = 10, maxBase = 16
For base_ As Uinteger = 2 To maxBase
    If Not isPrime(base_) Then
        Print "The first "; maxRhonda; " Rhonda numbers in base "; base_; ":"
        Dim As Uinteger rCount = 0
        Dim As Uinteger rhonda(1 To maxRhonda)
        Dim As Uinteger n = 1
        While rCount < maxRhonda
            If isRhonda(n, base_) Then
                rCount += 1
                rhonda(rCount) = n
            End If
            n += 1
        Wend
        Print "    in base 10: ";
        For i As Uinteger = 1 To maxRhonda
            Print " "; rhonda(i);
        Next i
        Print
        If base_ <> 10 Then
            Print Using "    in base ##: "; base_;
            For i As Uinteger = 1 To maxRhonda
                Print " "; ToBaseString(rhonda(i), base_);
            Next i
            Print
        End If
    End If
Next base_

Sleep
Output:
Same as ALGOL 68 entry.

Go

Translation of: Wren
Library: Go-rcu
package main

import (
    "fmt"
    "rcu"
    "strconv"
)

func contains(a []int, n int) bool {
    for _, e := range a {
        if e == n {
            return true
        }
    }
    return false
}

func main() {
    for b := 2; b <= 36; b++ {
        if rcu.IsPrime(b) {
            continue
        }
        count := 0
        var rhonda []int
        for n := 1; count < 15; n++ {
            digits := rcu.Digits(n, b)
            if !contains(digits, 0) {
                var anyEven = false
                for _, d := range digits {
                    if d%2 == 0 {
                        anyEven = true
                        break
                    }
                }
                if b != 10 || (contains(digits, 5) && anyEven) {
                    calc1 := 1
                    for _, d := range digits {
                        calc1 *= d
                    }
                    calc2 := b * rcu.SumInts(rcu.PrimeFactors(n))
                    if calc1 == calc2 {
                        rhonda = append(rhonda, n)
                        count++
                    }
                }
            }
        }
        if len(rhonda) > 0 {
            fmt.Printf("\nFirst 15 Rhonda numbers in base %d:\n", b)
            rhonda2 := make([]string, len(rhonda))
            counts2 := make([]int, len(rhonda))
            for i, r := range rhonda {
                rhonda2[i] = fmt.Sprintf("%d", r)
                counts2[i] = len(rhonda2[i])
            }
            rhonda3 := make([]string, len(rhonda))
            counts3 := make([]int, len(rhonda))
            for i, r := range rhonda {
                rhonda3[i] = strconv.FormatInt(int64(r), b)
                counts3[i] = len(rhonda3[i])
            }
            maxLen2 := rcu.MaxInts(counts2)
            maxLen3 := rcu.MaxInts(counts3)
            maxLen := maxLen2
            if maxLen3 > maxLen {
                maxLen = maxLen3
            }
            maxLen++
            fmt.Printf("In base 10: %*s\n", maxLen, rhonda2)
            fmt.Printf("In base %-2d: %*s\n", b, maxLen, rhonda3)
        }
    }
}
Output:
First 15 Rhonda numbers in base 4:
In base 10: [      10206       11935       12150       16031       45030       94185      113022      114415      191149      244713      259753      374782      392121      503773      649902]
In base 4 : [    2133132     2322133     2331312     3322133    22333212   112333221   123211332   123323233   232222231   323233221   333122221  1123133332  1133232321  1322333131  2132222232]

First 15 Rhonda numbers in base 6:
In base 10: [     855     1029     3813     5577     7040     7304    15104    19136    35350    36992    41031    42009    60368    65536    67821]
In base 6 : [    3543     4433    25353    41453    52332    53452   153532   224332   431354   443132   513543   522253  1143252  1223224  1241553]

First 15 Rhonda numbers in base 8:
In base 10: [   1836    6318    6622   10530   14500   14739   17655   18550   25398   25956   30562   39215   39325   50875   51429]
In base 8 : [   3454   14256   14736   24442   34244   34623   42367   44166   61466   62544   73542  114457  114635  143273  144345]

First 15 Rhonda numbers in base 9:
In base 10: [  15540   21054   25331   44360   44660   44733   47652   50560   54944   76857   77142   83334   83694   96448   97944]
In base 9 : [  23276   31783   37665   66758   67232   67323   72326   76317   83328  126376  126733  136273  136723  156264  158316]

First 15 Rhonda numbers in base 10:
In base 10: [  1568   2835   4752   5265   5439   5664   5824   5832   8526  12985  15625  15698  19435  25284  25662]
In base 10: [  1568   2835   4752   5265   5439   5664   5824   5832   8526  12985  15625  15698  19435  25284  25662]

First 15 Rhonda numbers in base 12:
In base 10: [   560    800   3993   4425   4602   4888   7315   8296   9315  11849  12028  13034  14828  15052  16264]
In base 12: [   3a8    568   2389   2689   27b6   29b4   4297   4974   5483   6a35   6b64   7662   86b8   8864   94b4]

First 15 Rhonda numbers in base 14:
In base 10: [  11475   18655   20565   29631   31725   45387   58404   58667   59950   63945   67525   68904   91245   99603  125543]
In base 14: [   4279    6b27    76cd    ab27    b7c1   1277d   173da   17547   17bc2   19437   1a873   1b17a   25377   28427   33a75]

First 15 Rhonda numbers in base 15:
In base 10: [  2392   2472  11468  15873  17424  18126  19152  20079  24388  30758  31150  33004  33550  37925  39483]
In base 15: [   a97    aec   35e8   4a83   5269   5586   5a1c   5e39   735d   91a8   936a   9ba4   9e1a   b385   ba73]

First 15 Rhonda numbers in base 16:
In base 10: [  1000   1134   6776  15912  19624  20043  20355  23946  26296  29070  31906  32292  34236  34521  36465]
In base 16: [   3e8    46e   1a78   3e28   4ca8   4e4b   4f83   5d8a   66b8   718e   7ca2   7e24   85bc   86d9   8e71]

First 15 Rhonda numbers in base 18:
In base 10: [  1470   3000   8918  17025  19402  20650  21120  22156  26522  36549  38354  43281  46035  48768  54229]
In base 18: [   49c    94c   1998   2g9f   35fg   39d4   3b36   3e6g   49f8   64e9   6a6e   77a9   7g19   8696   956d]

First 15 Rhonda numbers in base 20:
In base 10: [  1815  11050  15295  21165  22165  30702  34510  34645  42292  44165  52059  53416  65945  78430  80712]
In base 20: [   4af   17ca   1i4f   2ci5   2f85   3gf2   465a   46c5   55ec   5a85   6a2j   6dag   84h5   9g1a   a1fc]

First 15 Rhonda numbers in base 21:
In base 10: [  1632   5390   8512  12992  15678  25038  29412  34017  39552  48895  49147  61376  85078  89590  91798]
In base 21: [   3ef    c4e    j67   189e   1ebc   2eg6   33ec   3e2i   45e9   55i7   5697   6d3e   93j7   9e34   9j37]

First 15 Rhonda numbers in base 22:
In base 10: [   2695    4128    7865   28800   31710   37030   71875   74306  117760  117895  121626  126002  131427  175065  192753]
In base 22: [    5cb     8be     g5b    2fb2    2lb8    3ab4    6gb1    6lbc    b16g    b1cj    b96a    bi78    c7bl    g9fb    i25b]

First 15 Rhonda numbers in base 24:
In base 10: [  2080   2709   3976   5628   5656   7144   8296   9030  10094  17612  20559  24616  26224  29106  31458]
In base 24: [   3eg    4gl    6lg    9ic    9jg    c9g    e9g    fg6    hce   16dk   1bgf   1ihg   1lcg   22ci   26ei]

First 15 Rhonda numbers in base 25:
In base 10: [   6764    9633   13260   22022   53382   57640   66015   69006   97014  140130  142880  144235  159724  162565  165504]
In base 25: [    ake     fa8     l5a    1a5m    3aa7    3h5f    45ff    4aa6    655e    8o55    93f5    95ja    a5do    aa2f    aek4]

First 15 Rhonda numbers in base 26:
In base 10: [   7788    9322    9374   11160   22165   27885   34905   44785   47385   49257   62517   72709   74217  108745  132302]
In base 26: [    bde     dke     dme     gd6    16kd    1f6d    1pgd    2e6d    2i2d    2kmd    3ecd    43ed    45kd    64md    7die]

First 15 Rhonda numbers in base 27:
In base 10: [  4797  11844  12078  13200  14841  17750  24320  26883  27477  46455  52750  58581  61009  61446  61500]
In base 27: [   6fi    g6i    gf9    i2o    k9i    o9b   169k   19ni   1aii   29jf   2i9j   2q9i   32ig   337l   339l]

First 15 Rhonda numbers in base 28:
In base 10: [  3094   5808   5832   7462  11160  13671  27270  28194  28638  39375  39550  49500  50862  52338  52938]
In base 28: [   3qe    7bc    7c8    9ee    e6g    hc7   16lq   17qq   18em   1m67   1mce   273o   28oe   2al6   2bei]

First 15 Rhonda numbers in base 30:
In base 10: [  3024   3168   5115   5346   5950   6762   7750   7956   8470   9476   9576   9849  10360  11495  13035]
In base 30: [   3ao    3fi    5kf    5s6    6ia    7fc    8ia    8p6    9ca    afq    aj6    as9    bfa    cn5    eef]

First 15 Rhonda numbers in base 32:
In base 10: [  1944   3600  13520  15876  16732  16849  25410  25752  28951  47472  49610  50968  61596  64904  74005]
In base 32: [   1so    3gg    d6g    fg4    gas    geh    oq2    p4o    s8n   1ebg   1gea   1hoo   1s4s   1vc8   288l]

First 15 Rhonda numbers in base 33:
In base 10: [    756    7040    7568   13826   24930   30613   59345   63555   64372  131427  227840  264044  313709  336385  344858]
In base 33: [     mu     6fb     6vb     cmw     mtf     s3m    1lgb    1pbu    1q3m    3lml    6b78    7bfb    8o2b    9btg    9jm8]

First 15 Rhonda numbers in base 34:
In base 10: [   5661   14161   15620   16473   22185   37145  125579  134692  135405  138472  140369  177086  250665  255552  295614]
In base 34: [    4uh     c8h     dhe     e8h     j6h     w4h    36lh    3ehi    3f4h    3hqo    3jeh    4h6e    6csh    6h28    7hoi]

First 15 Rhonda numbers in base 35:
In base 10: [   8232    9476    9633   18634   30954   41905   52215   52440   56889   61992   62146   66339   98260  102180  103305]
In base 35: [    6p7     7pq     7u8     f7e     p9e     y7a    17lu    17sa    1bfe    1fl7    1fpl    1j5e    2a7f    2def    2ebk]

First 15 Rhonda numbers in base 36:
In base 10: [  1000   4800   5670   8190  10998  12412  13300  15750  16821  23016  51612  52734  67744  70929  75030]
In base 36: [    rs    3pc    4di    6bi    8hi    9ks    a9g    c5i    cz9    hrc   13to   14ou   1g9s   1iq9   1lw6]

J

tobase=: (a.{~;48 97(+ i.)each 10 26) {~ #.inv
isrhonda=: (*/@:(#.inv) = (* +/@q:))"0

task=: {{
  for_base.(#~ 0=1&p:) }.1+i.36 do.
    k=.i.0
    block=. 1+i.1e4
    while. 15>#k do.
      k=. k, block#~ base isrhonda block
      block=. block+1e4
    end.
    echo ''
    echo 'First 15 Rhondas in',b=.' base ',':',~":base
    echo 'In base 10: ',":15{.k
    echo 'In',;:inv b;base tobase each 15{.k
  end.
}}

   task''
Output:
First 15 Rhondas in base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhondas in base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhondas in base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhondas in base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhondas in base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhondas in base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4

First 15 Rhondas in base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75

First 15 Rhondas in base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73

First 15 Rhondas in base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71

First 15 Rhondas in base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d

First 15 Rhondas in base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc

First 15 Rhondas in base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37

First 15 Rhondas in base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b

First 15 Rhondas in base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei

First 15 Rhondas in base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4

First 15 Rhondas in base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die

First 15 Rhondas in base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l

First 15 Rhondas in base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei

First 15 Rhondas in base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef

First 15 Rhondas in base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l

First 15 Rhondas in base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8

First 15 Rhondas in base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi

First 15 Rhondas in base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk

First 15 Rhondas in base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6

Hoon

Library file (e.g. /lib/rhonda.hoon):

::
::  A library for producing Rhonda numbers and testing if numbers are Rhonda.
::
::    A number is Rhonda if the product of its digits of in base b equals 
::    the product of the base b and the sum of its prime factors.
::    see also: https://mathworld.wolfram.com/RhondaNumber.html
::
=<
::
|%
::  +check: test whether the number n is Rhonda to base b
::
++  check
  |=  [b=@ud n=@ud]
  ^-  ?
  ~_  leaf+"base b must be >= 2"
  ?>  (gte b 2)
  ~_  leaf+"candidate number n must be >= 2"
  ?>  (gte n 2)
  ::
  .=  (roll (base-digits b n) mul)
  %+  mul
    b
  (roll (prime-factors n) add)
::  +series: produce the first n numbers which are Rhonda in base b
::
::    produce ~ if base b has no Rhonda numbers
::
++  series
  |=  [b=@ud n=@ud]
  ^-  (list @ud)
  ~_  leaf+"base b must be >= 2"
  ?>  (gte b 2)
  ::
  ?:  =((prime-factors b) ~[b])
    ~
  =/  candidate=@ud  2
  =+  rhondas=*(list @ud)
  |-
  ?:  =(n 0)
    (flop rhondas)
  =/  is-rhonda=?  (check b candidate)
  %=  $
    rhondas    ?:(is-rhonda [candidate rhondas] rhondas)
    n          ?:(is-rhonda (dec n) n)
    candidate  +(candidate)
  ==
--
::
|%
::  +base-digits: produce a list of the digits of n represented in base b
::
::    This arm has two behaviors which may be at first surprising, but do not
::    matter for the purposes of the ++check and ++series arms, and allow for
::    some simplifications to its implementation.
::    - crashes on n=0
::    - orders the list of digits with least significant digits first
::
::    ex: (base-digits 4 10.206) produces ~[2 3 1 3 3 1 2]
::
++  base-digits
  |=  [b=@ud n=@ud]
  ^-  (list @ud)
  ?>  (gte b 2)
  ?<  =(n 0)
  ::
  |-
  ?:  =(n 0)
    ~
  :-  (mod n b)
  $(n (div n b))
::  +prime-factors: produce a list of the prime factors of n
::    
::    by trial division
::    n must be >= 2
::    if n is prime, produce ~[n]
::    ex: (prime-factors 10.206) produces ~[7 3 3 3 3 3 3 2]
::
++  prime-factors
  |=  [n=@ud]
  ^-  (list @ud)
  ?>  (gte n 2)
  ::
  =+  factors=*(list @ud)
  =/  wheel  new-wheel
  ::  test candidates as produced by the wheel, not exceeding sqrt(n) 
  ::
  |-
  =^  candidate  wheel  (next:wheel)
  ?.  (lte (mul candidate candidate) n)
    ?:((gth n 1) [n factors] factors)
  |-
  ?:  =((mod n candidate) 0)
    ::  repeat the prime factor as many times as possible
    ::
    $(factors [candidate factors], n (div n candidate))
  ^$
::  +new-wheel: a door for generating numbers that may be prime
::
::    This uses wheel factorization with a basis of {2, 3, 5} to limit the
::    number of composites produced. It produces numbers in increasing order
::    starting from 2.
::
++  new-wheel
  =/  fixed=(list @ud)  ~[2 3 5 7]
  =/  skips=(list @ud)  ~[4 2 4 2 4 6 2 6]
  =/  lent-fixed=@ud  (lent fixed)
  =/  lent-skips=@ud  (lent skips)
  ::
  |_  [current=@ud fixed-i=@ud skips-i=@ud]
  ::  +next: produce the next number and the new wheel state
  ::
  ++  next
    |.
    ::  Exhaust the numbers in fixed. Then calculate successive values by
    ::  cycling through skips and increasing from the previous number by
    ::  the current skip-value.
    ::
    =/  fixed-done=?  =(fixed-i lent-fixed)
    =/  next-fixed-i  ?:(fixed-done fixed-i +(fixed-i))
    =/  next-skips-i  ?:(fixed-done (mod +(skips-i) lent-skips) skips-i)
    =/  next
    ?.  fixed-done
      (snag fixed-i fixed)
    (add current (snag skips-i skips))
    :-  next
    +.$(current next, fixed-i next-fixed-i, skips-i next-skips-i)
  --
--

Script file ("generator") (e.g. /gen/rhonda.hoon):

/+  *rhonda
:-  %say
|=  [* [base=@ud many=@ud ~] ~]
:-  %noun
(series base many)

Alternative library file using map (associative array):

|%
++  check
  |=  [n=@ud base=@ud]
  ::  if base is prime, automatic no
  ::
  ?:  =((~(gut by (prime-map +(base))) base 0) 0)
    %.n
  ::  if not multiply the digits and compare to base x sum of factors
  ::
  ?:  =((roll (digits [base n]) mul) (mul base (roll (factor n) add)))
    %.y
  %.n
++  series
  |=  [base=@ud many=@ud]
  =/  rhondas  *(list @ud)
  ?:  =((~(gut by (prime-map +(base))) base 0) 0)
    rhondas
  =/  itr  1
  |-
  ?:  =((lent rhondas) many)
    (flop rhondas)
  ?:  =((check itr base) %.n)
    $(itr +(itr))
  $(rhondas [itr rhondas], itr +(itr))
::  digits: gives the list of digits of a number in a base
::
::    We strip digits least to most significant.
::    The least significant digit (lsd) of n in base b is just n mod b.
::    Subtract the lsd, divide by b, and repeat.
::    To know when to stop, we need to know how many digits there are.
++  digits
  |=  [base=@ud num=@ud]
  ^-  (list @ud)
  |-
  =/  modulus=@ud  (mod num base)
  ?:  =((num-digits base num) 1)
    ~[modulus]
  [modulus $(num (div (sub num modulus) base))]
::  num-digits: gives the number of digits of a number in a base
::
::    Simple idea: k is the number of digits of n in base b if and
::    only if k is the smallest number such that b^k > n.
++  num-digits
  |=  [base=@ud num=@ud]
  ^-  @ud
  =/  digits=@ud  1
  |-
  ?:  (gth (pow base digits) num)
    digits
  $(digits +(digits))
::  factor: produce a list of prime factors
::
::    The idea is to identify "small factors" of n, i.e. prime factors less than
::    the square root. We then divide n by these factors to reduce the
::    magnitude of n. It's easy to argue that after this is done, we obtain 1
::    or the largest prime factor.
::
++  factor
  |=  n=@ud
  ^-  (list @ud)
  ?:  ?|(=(n 0) =(n 1))
    ~[n]
  =/  factorization  *(list @ud)
  ::  produce primes less than or equal to root n
  ::
  =/  root  (sqrt n)
  =/  primes  (prime-map +(root))
  ::  itr = iterate; we want to iterate through the primes less than root n
  ::
  =/  itr  2
  |-
  ?:  =(itr +(root))
  ::  if n is now 1 we're done
  ::
    ?:  =(n 1)
      factorization
    ::  otherwise it's now the original n's largest primes factor
    ::
    [n factorization]
  ::  if itr not prime move on
  ::
  ?:  =((~(gut by primes) itr 0) 1)
    $(itr +(itr))
  ::  if it is prime, divide out by the highest power that divides num
  ::
  ?:  =((mod n itr) 0)
    $(n (div n itr), factorization [itr factorization])
  ::  once done, move to next prime
  ::
  $(itr +(itr))
::  sqrt: gives the integer square root of a number
::
::    It's based on an algorithm that predates the Greeks:
::    To find the square root of A, think of A as an area.
::    Guess the side of the square x. Compute the other side y = A/x.
::    If x is an over/underestimate then y is an under/overestimate.
::    So (x+y)/2 is the average of an over and underestimate, thus better than x.
::    Repeatedly doing x --> (x + A/x)/2 converges to sqrt(A).
::
::    This algorithm is the same but with integer valued operations.
::    The algorithm either converges to the integer square root and repeats,
::    or gets trapped in a two-cycle of adjacent integers.
::    In the latter case, the smaller number is the answer.
::
++  sqrt
  |=  n=@ud
  =/  guess=@ud  1
  |-
  =/  new-guess  (div (add guess (div n guess)) 2)
  ::  sequence stabilizes
  ::
  ?:  =(guess new-guess)
    guess
  ::  sequence is trapped in 2-cycle
  ::
  ?:  =(guess +(new-guess))
    new-guess
  ?:  =(new-guess +(guess))
    guess
  $(guess new-guess)
::  prime-map: (effectively) produces primes less than a given input
::
::    This is the sieve of Eratosthenes to produce primes less than n.
::    I used a map because it had much faster performance than a list.
::    Any key in the map is a non-prime. The value 1 indicates "false."
::    I.e. it's not a prime.
++  prime-map
  |=  n=@ud
  ^-  (map @ud @ud)
  =/  prime-map  `(map @ud @ud)`(my ~[[0 1] [1 1]])
  ::  start sieving with 2
  ::
  =/  sieve  2
  |-
  ::  if sieve is too large to be a factor we're done
  ::
  ?:  (gte (mul sieve sieve) n)
    prime-map
  ::  if not too large but not prime, move on
  ::
  ?:  =((~(gut by prime-map) sieve 0) 1)
    $(sieve +(sieve))
  ::  sequence: explanation
  ::
  ::    If s is the sieve number, we start sieving multiples
  ::    of s at s^2 in sequence: s^2, s^2 + s, s^2 + 2s, ...
  ::    We start at s^2 because any number smaller than s^2
  ::    has prime factors less than s and would have been
  ::    eliminated earlier in the sieving process.
  ::
  =/  sequence  (mul sieve sieve)
  |-
  ::  done sieving with s once sequence is past n
  ::
  ?:  (gte sequence n)
    ^$(sieve +(sieve))
  ::  if sequence position is known not prime we move on
  ::
  ?:  =((~(gut by prime-map) sequence 0) 1)
    $(sequence (add sequence sieve))
  ::  otherwise we mark position of sequence as not prime and move on
  ::
  $(prime-map (~(put by prime-map) sequence 1), sequence (add sequence sieve))
--

Java

public class RhondaNumbers {
    public static void main(String[] args) {
        final int limit = 15;
        for (int base = 2; base <= 36; ++base) {
            if (isPrime(base))
                continue;
            System.out.printf("First %d Rhonda numbers to base %d:\n", limit, base);
            int numbers[] = new int[limit];
            for (int n = 1, count = 0; count < limit; ++n) {
                if (isRhonda(base, n))
                    numbers[count++] = n;
            }
            System.out.printf("In base 10:");
            for (int i = 0; i < limit; ++i)
                System.out.printf(" %d", numbers[i]);
            System.out.printf("\nIn base %d:", base);
            for (int i = 0; i < limit; ++i)
                System.out.printf(" %s", Integer.toString(numbers[i], base));
            System.out.printf("\n\n");
        }
    }
    
    private static int digitProduct(int base, int n) {
        int product = 1;
        for (; n != 0; n /= base)
            product *= n % base;
        return product;
    }
     
    private static int primeFactorSum(int n) {
        int sum = 0;
        for (; (n & 1) == 0; n >>= 1)
            sum += 2;
        for (int p = 3; p * p <= n; p += 2)
            for (; n % p == 0; n /= p)
                sum += p;
        if (n > 1)
            sum += n;
        return sum;
    }
     
    private static boolean isPrime(int n) {
        if (n < 2)
            return false;
        if (n % 2 == 0)
            return n == 2;
        if (n % 3 == 0)
            return n == 3;
        for (int p = 5; p * p <= n; p += 4) {
            if (n % p == 0)
                return false;
            p += 2;
            if (n % p == 0)
                return false;
        }
        return true;
    }
     
    private static boolean isRhonda(int base, int n) {
        return digitProduct(base, n) == base * primeFactorSum(n);
    }
}
Output:
First 15 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4

First 15 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75

First 15 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73

First 15 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71

First 15 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d

First 15 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc

First 15 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37

First 15 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b

First 15 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei

First 15 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4

First 15 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die

First 15 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l

First 15 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei

First 15 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef

First 15 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l

First 15 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8

First 15 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi

First 15 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk

First 15 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6

jq

Works with jq and gojq, that is, the C and Go implementations of jq.

Adapted from Wren

Generic stream-oriented utility functions

def prod(s): reduce s as $_ (1; . * $_);

def sigma(s): reduce s as $_ (0; . + $_);

# If s is a stream of JSON entities that does not include null, butlast(s) emits all but the last.
def butlast(s):
  label $out
  | foreach (s,null) as $x ({};
     if $x == null then break $out else .emit = .prev | .prev = $x end)
  | select(.emit).emit;

def multiple(s):
  first(foreach s as $x (0; .+1; select(. > 1))) // false;

# Output: a stream of the prime factors of the input
# e.g.
#  2 | factors #=> 2
# 24 | factors #=> 2 2 2 3
def factors:
  . as $in 
  | [2, $in, false]
  | recurse(
      . as [$p, $q, $valid, $s]
      | if $q == 1        then empty
        elif $q % $p == 0 then [$p, $q/$p, true]
        elif $p == 2      then [3, $q, false, $s]
        else ($s // ($q | sqrt)) as $s
        | if $p + 2 <= $s then [$p + 2, $q, false, $s]
          else [$q, 1, true]
          end
        end )
   | if .[2] then .[0] else empty end ;

Other generic functions

def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;

def is_prime:
  multiple(factors) | not;
  
def tobase($b):
  def digit: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[.:.+1];
  def mod: . % $b;
  def div: ((. - mod) / $b);
  def digits: recurse( select(. > 0) | div) | mod ;
  # For jq it would be wise to protect against `infinite` as input, but using `isinfinite` confuses gojq
  select( (tostring|test("^[0-9]+$")) and 2 <= $b and $b <= 36)
  | if . == 0 then "0"
    else [digits | digit] | reverse[1:] | add
    end;

# emit the decimal values of the "digits"
def digits($b):
  def mod: . % $b;
  def div: ((. - mod) / $b);
  butlast(recurse( select(. > 0) | div) | mod) ;

Rhonda numbers

# Emit a stream of Rhonda numbers in the given base
def rhondas($b):
  range(1; infinite) as $n
  | ($n | [digits($b)]) as $digits
  | select($digits|index(0)|not)
  | select(($b != 10) or (($digits|index(5)) and ($digits | any(. % 2 == 0))))
  | select(prod($digits[]) == ($b * sigma($n | factors))) 
  | $n ;

The task

def task($count):
  range (2; 37) as $b
  | select( $b | is_prime | not)
  | [ limit($count; rhondas($b)) ]
  | select(length > 0)
  |"First \($count) Rhonda numbers in base \($b):",
    (   (map(tostring)) as $rhonda2
      | (map(tobase($b))) as $rhonda3
      | (($rhonda2|map(length)) | max) as $maxLen2
      | (($rhonda3|map(length)) | max) as $maxLen3
      | ( ([$maxLen2, $maxLen3]|max) + 1) as $maxLen
      | "In base 10:  \($rhonda2 | map(lpad($maxLen)) | join(" ") )",
        "In base \($b|lpad(2)):  \($rhonda3 | map(lpad($maxLen)) | join(" ") )",
        "") ;

task(10)
Output:
First 10 Rhonda numbers in base 4:
In base 10:       10206      11935      12150      16031      45030      94185     113022     114415     191149     244713
In base  4:     2133132    2322133    2331312    3322133   22333212  112333221  123211332  123323233  232222231  323233221

First 10 Rhonda numbers in base 6:
In base 10:      855    1029    3813    5577    7040    7304   15104   19136   35350   36992
In base  6:     3543    4433   25353   41453   52332   53452  153532  224332  431354  443132

First 10 Rhonda numbers in base 8:
In base 10:    1836   6318   6622  10530  14500  14739  17655  18550  25398  25956
In base  8:    3454  14256  14736  24442  34244  34623  42367  44166  61466  62544

First 10 Rhonda numbers in base 9:
In base 10:    15540   21054   25331   44360   44660   44733   47652   50560   54944   76857
In base  9:    23276   31783   37665   66758   67232   67323   72326   76317   83328  126376

First 10 Rhonda numbers in base 10:
In base 10:    1568   2835   4752   5265   5439   5664   5824   5832   8526  12985
In base 10:    1568   2835   4752   5265   5439   5664   5824   5832   8526  12985

First 10 Rhonda numbers in base 12:
In base 10:     560    800   3993   4425   4602   4888   7315   8296   9315  11849
In base 12:     3A8    568   2389   2689   27B6   29B4   4297   4974   5483   6A35

First 10 Rhonda numbers in base 14:
In base 10:   11475  18655  20565  29631  31725  45387  58404  58667  59950  63945
In base 14:    4279   6B27   76CD   AB27   B7C1  1277D  173DA  17547  17BC2  19437

First 10 Rhonda numbers in base 15:
In base 10:    2392   2472  11468  15873  17424  18126  19152  20079  24388  30758
In base 15:     A97    AEC   35E8   4A83   5269   5586   5A1C   5E39   735D   91A8

First 10 Rhonda numbers in base 16:
In base 10:    1000   1134   6776  15912  19624  20043  20355  23946  26296  29070
In base 16:     3E8    46E   1A78   3E28   4CA8   4E4B   4F83   5D8A   66B8   718E

First 10 Rhonda numbers in base 18:
In base 10:    1470   3000   8918  17025  19402  20650  21120  22156  26522  36549
In base 18:     49C    94C   1998   2G9F   35FG   39D4   3B36   3E6G   49F8   64E9

First 10 Rhonda numbers in base 20:
In base 10:    1815  11050  15295  21165  22165  30702  34510  34645  42292  44165
In base 20:     4AF   17CA   1I4F   2CI5   2F85   3GF2   465A   46C5   55EC   5A85

First 10 Rhonda numbers in base 21:
In base 10:    1632   5390   8512  12992  15678  25038  29412  34017  39552  48895
In base 21:     3EF    C4E    J67   189E   1EBC   2EG6   33EC   3E2I   45E9   55I7

First 10 Rhonda numbers in base 22:
In base 10:     2695    4128    7865   28800   31710   37030   71875   74306  117760  117895
In base 22:      5CB     8BE     G5B    2FB2    2LB8    3AB4    6GB1    6LBC    B16G    B1CJ

First 10 Rhonda numbers in base 24:
In base 10:    2080   2709   3976   5628   5656   7144   8296   9030  10094  17612
In base 24:     3EG    4GL    6LG    9IC    9JG    C9G    E9G    FG6    HCE   16DK

First 10 Rhonda numbers in base 25:
In base 10:     6764    9633   13260   22022   53382   57640   66015   69006   97014  140130
In base 25:      AKE     FA8     L5A    1A5M    3AA7    3H5F    45FF    4AA6    655E    8O55

First 10 Rhonda numbers in base 26:
In base 10:    7788   9322   9374  11160  22165  27885  34905  44785  47385  49257
In base 26:     BDE    DKE    DME    GD6   16KD   1F6D   1PGD   2E6D   2I2D   2KMD

First 10 Rhonda numbers in base 27:
In base 10:    4797  11844  12078  13200  14841  17750  24320  26883  27477  46455
In base 27:     6FI    G6I    GF9    I2O    K9I    O9B   169K   19NI   1AII   29JF

First 10 Rhonda numbers in base 28:
In base 10:    3094   5808   5832   7462  11160  13671  27270  28194  28638  39375
In base 28:     3QE    7BC    7C8    9EE    E6G    HC7   16LQ   17QQ   18EM   1M67

First 10 Rhonda numbers in base 30:
In base 10:   3024  3168  5115  5346  5950  6762  7750  7956  8470  9476
In base 30:    3AO   3FI   5KF   5S6   6IA   7FC   8IA   8P6   9CA   AFQ

First 10 Rhonda numbers in base 32:
In base 10:    1944   3600  13520  15876  16732  16849  25410  25752  28951  47472
In base 32:     1SO    3GG    D6G    FG4    GAS    GEH    OQ2    P4O    S8N   1EBG

First 10 Rhonda numbers in base 33:
In base 10:      756    7040    7568   13826   24930   30613   59345   63555   64372  131427
In base 33:       MU     6FB     6VB     CMW     MTF     S3M    1LGB    1PBU    1Q3M    3LML

First 10 Rhonda numbers in base 34:
In base 10:     5661   14161   15620   16473   22185   37145  125579  134692  135405  138472
In base 34:      4UH     C8H     DHE     E8H     J6H     W4H    36LH    3EHI    3F4H    3HQO

First 10 Rhonda numbers in base 35:
In base 10:    8232   9476   9633  18634  30954  41905  52215  52440  56889  61992
In base 35:     6P7    7PQ    7U8    F7E    P9E    Y7A   17LU   17SA   1BFE   1FL7

First 10 Rhonda numbers in base 36:
In base 10:    1000   4800   5670   8190  10998  12412  13300  15750  16821  23016
In base 36:      RS    3PC    4DI    6BI    8HI    9KS    A9G    C5I    CZ9    HRC

Julia

using Primes

isRhonda(n, b) = prod(digits(n, base=b)) == b * sum([prod(pair) for pair in factor(n).pe])

function displayrhondas(low, high, nshow)
    for b in filter(!isprime, low:high)
        n, rhondas = 1, Int[]
        while length(rhondas) < nshow
            isRhonda(n, b) && push!(rhondas, n)
            n += 1
        end
        println("First $nshow Rhondas in base $b:")
        println("In base 10: ", rhondas)
        println("In base $b: ", replace(string([string(i, base=b) for i in rhondas]), "\"" => ""), "\n")
    end
end

displayrhondas(2, 16, 15)
Output:
First 15 Rhondas in base 4:
In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902]
In base 4: [2133132, 2322133, 2331312, 3322133, 22333212, 112333221, 123211332, 123323233, 232222231, 323233221, 333122221, 1123133332, 1133232321, 1322333131, 2132222232]

First 15 Rhondas in base 6:
In base 10: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821]
In base 6: [3543, 4433, 25353, 41453, 52332, 53452, 153532, 224332, 431354, 443132, 513543, 522253, 1143252, 1223224, 1241553]

First 15 Rhondas in base 8:
In base 10: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429]
In base 8: [3454, 14256, 14736, 24442, 34244, 34623, 42367, 44166, 61466, 62544, 73542, 114457, 114635, 143273, 144345]

First 15 Rhondas in base 9:
In base 10: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944]
In base 9: [23276, 31783, 37665, 66758, 67232, 67323, 72326, 76317, 83328, 126376, 126733, 136273, 136723, 156264, 158316]

First 15 Rhondas in base 10:
In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662]
In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662]

First 15 Rhondas in base 12:
In base 10: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264]
In base 12: [3a8, 568, 2389, 2689, 27b6, 29b4, 4297, 4974, 5483, 6a35, 6b64, 7662, 86b8, 8864, 94b4]

First 15 Rhondas in base 14:
In base 10: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543]
In base 14: [4279, 6b27, 76cd, ab27, b7c1, 1277d, 173da, 17547, 17bc2, 19437, 1a873, 1b17a, 25377, 28427, 33a75]

First 15 Rhondas in base 15:
In base 10: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483]
In base 15: [a97, aec, 35e8, 4a83, 5269, 5586, 5a1c, 5e39, 735d, 91a8, 936a, 9ba4, 9e1a, b385, ba73]

First 15 Rhondas in base 16:
In base 10: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465]
In base 16: [3e8, 46e, 1a78, 3e28, 4ca8, 4e4b, 4f83, 5d8a, 66b8, 718e, 7ca2, 7e24, 85bc, 86d9, 8e71]

Mathematica/Wolfram Language

ClearAll[RhondaNumberQ]
RhondaNumberQ[b_Integer][n_Integer] := Module[{l, r},
  l = Times @@ IntegerDigits[n, b];
  r = Total[Catenate[ConstantArray @@@ FactorInteger[n]]];
  l == b r
]
bases = Select[Range[2, 36], PrimeQ/*Not];
Do[
 Print["base ", b, ":", Take[Select[Range[700000], RhondaNumberQ[b]], UpTo[15]]];
 ,
 {b, bases}
]
Output:
base 4:{10206,11935,12150,16031,45030,94185,113022,114415,191149,244713,259753,374782,392121,503773,649902}
base 6:{855,1029,3813,5577,7040,7304,15104,19136,35350,36992,41031,42009,60368,65536,67821}
base 8:{1836,6318,6622,10530,14500,14739,17655,18550,25398,25956,30562,39215,39325,50875,51429}
base 9:{15540,21054,25331,44360,44660,44733,47652,50560,54944,76857,77142,83334,83694,96448,97944}
base 10:{1568,2835,4752,5265,5439,5664,5824,5832,8526,12985,15625,15698,19435,25284,25662}
base 12:{560,800,3993,4425,4602,4888,7315,8296,9315,11849,12028,13034,14828,15052,16264}
base 14:{11475,18655,20565,29631,31725,45387,58404,58667,59950,63945,67525,68904,91245,99603,125543}
base 15:{2392,2472,11468,15873,17424,18126,19152,20079,24388,30758,31150,33004,33550,37925,39483}
base 16:{1000,1134,6776,15912,19624,20043,20355,23946,26296,29070,31906,32292,34236,34521,36465}
base 18:{1470,3000,8918,17025,19402,20650,21120,22156,26522,36549,38354,43281,46035,48768,54229}
base 20:{1815,11050,15295,21165,22165,30702,34510,34645,42292,44165,52059,53416,65945,78430,80712}
base 21:{1632,5390,8512,12992,15678,25038,29412,34017,39552,48895,49147,61376,85078,89590,91798}
base 22:{2695,4128,7865,28800,31710,37030,71875,74306,117760,117895,121626,126002,131427,175065,192753}
base 24:{2080,2709,3976,5628,5656,7144,8296,9030,10094,17612,20559,24616,26224,29106,31458}
base 25:{6764,9633,13260,22022,53382,57640,66015,69006,97014,140130,142880,144235,159724,162565,165504}
base 26:{7788,9322,9374,11160,22165,27885,34905,44785,47385,49257,62517,72709,74217,108745,132302}
base 27:{4797,11844,12078,13200,14841,17750,24320,26883,27477,46455,52750,58581,61009,61446,61500}
base 28:{3094,5808,5832,7462,11160,13671,27270,28194,28638,39375,39550,49500,50862,52338,52938}
base 30:{3024,3168,5115,5346,5950,6762,7750,7956,8470,9476,9576,9849,10360,11495,13035}
base 32:{1944,3600,13520,15876,16732,16849,25410,25752,28951,47472,49610,50968,61596,64904,74005}
base 33:{756,7040,7568,13826,24930,30613,59345,63555,64372,131427,227840,264044,313709,336385,344858}
base 34:{5661,14161,15620,16473,22185,37145,125579,134692,135405,138472,140369,177086,250665,255552,295614}
base 35:{8232,9476,9633,18634,30954,41905,52215,52440,56889,61992,62146,66339,98260,102180,103305}
base 36:{1000,4800,5670,8190,10998,12412,13300,15750,16821,23016,51612,52734,67744,70929,75030}

Nim

import std/[sequtils, strformat, strutils]

type Base = 2..36

template isEven(n: int): bool = (n and 1) == 0

func isPrime(n: Natural): bool =
  ## Return true if "n" is prime.
  if n < 2: return false
  if n.isEven: return n == 2
  if n mod 3 == 0: return n == 3
  var d = 5
  while d * d <= n:
    if n mod d == 0: return false
    inc d, 2
  return true

func digitProduct(n: Positive; base: Base): int =
  ## Return the product of digits of "n" in given base.
  var n = n.Natural
  result = 1
  while n != 0:
    result *= n mod base
    n = n div base

func primeFactorSum(n: Positive): int =
  ## Return the sum of prime factors of "n".
  var n = n.Natural
  while n.isEven:
    inc result, 2
    n  = n shr 1
  var d = 3
  while d * d <= n:
    while n mod d == 0:
      inc result, d
      n = n div d
    inc d, 2
  if n > 1: inc result, n

func isRhondaNumber(n: Positive; base: Base): bool =
  ## Return true if "n" is a Rhonda number to given base.
  n.digitProduct(base) == base * n.primeFactorSum

const Digits = toSeq('0'..'9') & toSeq('a'..'z')

func toBase(n: Positive; base: Base): string =
  ## Return the string representation of "n" in given base.
  var n = n.Natural
  while true:
    result.add Digits[n mod base]
    n = n div base
    if n == 0: break
  # Reverse the digits.
  for i in 1..(result.len shr 1):
    swap result[i - 1], result[^i]


const N = 10

for base in 2..36:
  if base.isPrime: continue
  echo &"First {N} Rhonda numbers to base {base}:"
  var rhondaList: seq[Positive]
  var n = 1
  var count = 0
  while count < N:
    if n.isRhondaNumber(base):
      rhondaList.add n
      inc count
    inc n
  echo "In base 10: ", rhondaList.join(" ")
  echo &"In base {base}: ", rhondaList.mapIt(it.toBase(base)).join(" ")
  echo()
Output:
First 10 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221

First 10 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132

First 10 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544

First 10 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376

First 10 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985

First 10 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35

First 10 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437

First 10 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8

First 10 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e

First 10 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9

First 10 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85

First 10 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7

First 10 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj

First 10 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk

First 10 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55

First 10 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd

First 10 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf

First 10 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67

First 10 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq

First 10 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg

First 10 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml

First 10 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo

First 10 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7

First 10 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc

PARI/GP

Translation of: Julia
isRhonda(n, b) =
{
    local(mydigits, product, mysum, factors, pairProduct);
    
    mydigits = digits(n, b);
    product = vecprod(mydigits);
    factors = factor(n);
    mysum= 0;
    for(i = 1, matsize(factors)[1],
        pairProduct = factors[i, 1] * factors[i, 2];
        mysum += pairProduct;
    );
    product == b * mysum;
}

displayrhondas(low, high, nshow) =
{
    local(b, n, rhondas, count, basebRhondas);
    for(b = low, high,
        if(isprime(b), next);
        n = 1; rhondas = [];
        count = 0;
        while(count < nshow,
            if(isRhonda(n, b),
                rhondas = concat(rhondas, n);
                count++;
            );
            n++;
        );
        print("First " nshow " Rhondas in base " b ":");
        print("In base 10: " rhondas);
        basebRhondas = vector(#rhondas, i, (digits(rhondas[i], b)));
        print("In base " b ": " basebRhondas);
        print("\n");
    );
}

displayrhondas(2, 16, 15);
Output:
First 15 Rhondas in base 4:
In base 10: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902]
In base 4: [[2, 1, 3, 3, 1, 3, 2], [2, 3, 2, 2, 1, 3, 3], [2, 3, 3, 1, 3, 1, 2], [3, 3, 2, 2, 1, 3, 3], [2, 2, 3, 3, 3, 2, 1, 2], [1, 1, 2, 3, 3, 3, 2, 2, 1], [1, 2, 3, 2, 1, 1, 3, 3, 2], [1, 2, 3, 3, 2, 3, 2, 3, 3], [2, 3, 2, 2, 2, 2, 2, 3, 1], [3, 2, 3, 2, 3, 3, 2, 2, 1], [3, 3, 3, 1, 2, 2, 2, 2, 1], [1, 1, 2, 3, 1, 3, 3, 3, 3, 2], [1, 1, 3, 3, 2, 3, 2, 3, 2, 1], [1, 3, 2, 2, 3, 3, 3, 1, 3, 1], [2, 1, 3, 2, 2, 2, 2, 2, 3, 2]]


First 15 Rhondas in base 6:
In base 10: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821]
In base 6: [[3, 5, 4, 3], [4, 4, 3, 3], [2, 5, 3, 5, 3], [4, 1, 4, 5, 3], [5, 2, 3, 3, 2], [5, 3, 4, 5, 2], [1, 5, 3, 5, 3, 2], [2, 2, 4, 3, 3, 2], [4, 3, 1, 3, 5, 4], [4, 4, 3, 1, 3, 2], [5, 1, 3, 5, 4, 3], [5, 2, 2, 2, 5, 3], [1, 1, 4, 3, 2, 5, 2], [1, 2, 2, 3, 2, 2, 4], [1, 2, 4, 1, 5, 5, 3]]


First 15 Rhondas in base 8:
In base 10: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429]
In base 8: [[3, 4, 5, 4], [1, 4, 2, 5, 6], [1, 4, 7, 3, 6], [2, 4, 4, 4, 2], [3, 4, 2, 4, 4], [3, 4, 6, 2, 3], [4, 2, 3, 6, 7], [4, 4, 1, 6, 6], [6, 1, 4, 6, 6], [6, 2, 5, 4, 4], [7, 3, 5, 4, 2], [1, 1, 4, 4, 5, 7], [1, 1, 4, 6, 3, 5], [1, 4, 3, 2, 7, 3], [1, 4, 4, 3, 4, 5]]


First 15 Rhondas in base 9:
In base 10: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944]
In base 9: [[2, 3, 2, 7, 6], [3, 1, 7, 8, 3], [3, 7, 6, 6, 5], [6, 6, 7, 5, 8], [6, 7, 2, 3, 2], [6, 7, 3, 2, 3], [7, 2, 3, 2, 6], [7, 6, 3, 1, 7], [8, 3, 3, 2, 8], [1, 2, 6, 3, 7, 6], [1, 2, 6, 7, 3, 3], [1, 3, 6, 2, 7, 3], [1, 3, 6, 7, 2, 3], [1, 5, 6, 2, 6, 4], [1, 5, 8, 3, 1, 6]]


First 15 Rhondas in base 10:
In base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662]
In base 10: [[1, 5, 6, 8], [2, 8, 3, 5], [4, 7, 5, 2], [5, 2, 6, 5], [5, 4, 3, 9], [5, 6, 6, 4], [5, 8, 2, 4], [5, 8, 3, 2], [8, 5, 2, 6], [1, 2, 9, 8, 5], [1, 5, 6, 2, 5], [1, 5, 6, 9, 8], [1, 9, 4, 3, 5], [2, 5, 2, 8, 4], [2, 5, 6, 6, 2]]


First 15 Rhondas in base 12:
In base 10: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264]
In base 12: [[3, 10, 8], [5, 6, 8], [2, 3, 8, 9], [2, 6, 8, 9], [2, 7, 11, 6], [2, 9, 11, 4], [4, 2, 9, 7], [4, 9, 7, 4], [5, 4, 8, 3], [6, 10, 3, 5], [6, 11, 6, 4], [7, 6, 6, 2], [8, 6, 11, 8], [8, 8, 6, 4], [9, 4, 11, 4]]


First 15 Rhondas in base 14:
In base 10: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543]
In base 14: [[4, 2, 7, 9], [6, 11, 2, 7], [7, 6, 12, 13], [10, 11, 2, 7], [11, 7, 12, 1], [1, 2, 7, 7, 13], [1, 7, 3, 13, 10], [1, 7, 5, 4, 7], [1, 7, 11, 12, 2], [1, 9, 4, 3, 7], [1, 10, 8, 7, 3], [1, 11, 1, 7, 10], [2, 5, 3, 7, 7], [2, 8, 4, 2, 7], [3, 3, 10, 7, 5]]


First 15 Rhondas in base 15:
In base 10: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483]
In base 15: [[10, 9, 7], [10, 14, 12], [3, 5, 14, 8], [4, 10, 8, 3], [5, 2, 6, 9], [5, 5, 8, 6], [5, 10, 1, 12], [5, 14, 3, 9], [7, 3, 5, 13], [9, 1, 10, 8], [9, 3, 6, 10], [9, 11, 10, 4], [9, 14, 1, 10], [11, 3, 8, 5], [11, 10, 7, 3]]


First 15 Rhondas in base 16:
In base 10: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465]
In base 16: [[3, 14, 8], [4, 6, 14], [1, 10, 7, 8], [3, 14, 2, 8], [4, 12, 10, 8], [4, 14, 4, 11], [4, 15, 8, 3], [5, 13, 8, 10], [6, 6, 11, 8], [7, 1, 8, 14], [7, 12, 10, 2], [7, 14, 2, 4], [8, 5, 11, 12], [8, 6, 13, 9], [8, 14, 7, 1]]



Perl

Library: ntheory
use strict;
use warnings;
use feature 'say';
use ntheory qw<is_prime factor vecsum vecprod todigitstring todigits>;

sub rhonda {
    my($b, $cnt) = @_;
    my(@r,$n);
    while (++$n) {
        push @r, $n if ($b * vecsum factor($n)) == vecprod todigits($n,$b);
        return @r if $cnt == @r;
    }
}

for my $b (grep { ! is_prime $_ } 2..36) {
    my @Rb = map { todigitstring($_,$b) } my @R = rhonda($b, 15);
    say <<~EOT;
        First 15 Rhonda numbers to base $b:
        In base $b: @Rb
        In base 10: @R
        EOT
}
Output:
First 15 Rhonda numbers to base 4:
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902

First 15 Rhonda numbers to base 6:
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821

First 15 Rhonda numbers to base 8:
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429

First 15 Rhonda numbers to base 9:
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944

First 15 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers to base 12:
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264

First 15 Rhonda numbers to base 14:
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543

First 15 Rhonda numbers to base 15:
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483

First 15 Rhonda numbers to base 16:
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465

First 15 Rhonda numbers to base 18:
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229

First 15 Rhonda numbers to base 20:
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712

First 15 Rhonda numbers to base 21:
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798

First 15 Rhonda numbers to base 22:
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753

First 15 Rhonda numbers to base 24:
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458

First 15 Rhonda numbers to base 25:
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504

First 15 Rhonda numbers to base 26:
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302

First 15 Rhonda numbers to base 27:
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500

First 15 Rhonda numbers to base 28:
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
First 15 Rhonda numbers to base 30:
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035

First 15 Rhonda numbers to base 32:
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005

First 15 Rhonda numbers to base 33:
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858

First 15 Rhonda numbers to base 34:
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614

First 15 Rhonda numbers to base 35:
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305

First 15 Rhonda numbers to base 36:
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030

Phix

with javascript_semantics
constant fmt = """
First 15 Rhonda numbers in base %d:
In base 10:  %s
In base %-2d:  %s

"""
function digit(integer d) return d-iff(d<='9'?'0':'a'-10) end function

for base=2 to 36 do
    if not is_prime(base) then
        sequence rhondab = {},  -- (base)
                 rhondad = {}   -- (decimal)
        integer n = 1
        while length(rhondab)<15 do
            string digits = sprintf("%a",{{base,n}})
            if not find('0',digits)
            and (base!=10 or (find('5',digits) and sum(apply(digits,even))!=0)) then
                integer pd = product(apply(digits,digit)),
                        bs = base*sum(prime_factors(n,true,-1))
                if pd==bs then
                    string decdig = sprintf("%d",n)
                    integer l = max(length(decdig),length(digits))
                    rhondab = append(rhondab,pad_head(digits,l))
                    rhondad = append(rhondad,pad_head(decdig,l))
                end if
            end if
            n += 1
        end while
        printf(1,fmt,{base,join(rhondad),base,join(rhondab)})
    end if
end for
Output:
First 15 Rhonda numbers in base 4:
In base 10:    10206   11935   12150   16031    45030     94185    113022    114415    191149    244713    259753     374782     392121     503773     649902
In base 4 :  2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhonda numbers in base 6:
In base 10:   855 1029  3813  5577  7040  7304  15104  19136  35350  36992  41031  42009   60368   65536   67821
In base 6 :  3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhonda numbers in base 8:
In base 10:  1836  6318  6622 10530 14500 14739 17655 18550 25398 25956 30562  39215  39325  50875  51429
In base 8 :  3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhonda numbers in base 9:
In base 10:  15540 21054 25331 44360 44660 44733 47652 50560 54944  76857  77142  83334  83694  96448  97944
In base 9 :  23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhonda numbers in base 10:
In base 10:  1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10:  1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers in base 12:
In base 10:  560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12:  3a8 568 2389 2689 27b6 29b4 4297 4974 5483  6a35  6b64  7662  86b8  8864  94b4

First 15 Rhonda numbers in base 14:
In base 10:  11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14:   4279  6b27  76cd  ab27  b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427  33a75

First 15 Rhonda numbers in base 15:
In base 10:  2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15:   a97  aec  35e8  4a83  5269  5586  5a1c  5e39  735d  91a8  936a  9ba4  9e1a  b385  ba73

First 15 Rhonda numbers in base 16:
In base 10:  1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16:   3e8  46e 1a78  3e28  4ca8  4e4b  4f83  5d8a  66b8  718e  7ca2  7e24  85bc  86d9  8e71

First 15 Rhonda numbers in base 18:
In base 10:  1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18:   49c  94c 1998  2g9f  35fg  39d4  3b36  3e6g  49f8  64e9  6a6e  77a9  7g19  8696  956d

First 15 Rhonda numbers in base 20:
In base 10:  1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20:   4af  17ca  1i4f  2ci5  2f85  3gf2  465a  46c5  55ec  5a85  6a2j  6dag  84h5  9g1a  a1fc

First 15 Rhonda numbers in base 21:
In base 10:  1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21:   3ef  c4e  j67  189e  1ebc  2eg6  33ec  3e2i  45e9  55i7  5697  6d3e  93j7  9e34  9j37

First 15 Rhonda numbers in base 22:
In base 10:  2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22:   5cb  8be  g5b  2fb2  2lb8  3ab4  6gb1  6lbc   b16g   b1cj   b96a   bi78   c7bl   g9fb   i25b

First 15 Rhonda numbers in base 24:
In base 10:  2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24:   3eg  4gl  6lg  9ic  9jg  c9g  e9g  fg6   hce  16dk  1bgf  1ihg  1lcg  22ci  26ei

First 15 Rhonda numbers in base 25:
In base 10:  6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25:   ake  fa8   l5a  1a5m  3aa7  3h5f  45ff  4aa6  655e   8o55   93f5   95ja   a5do   aa2f   aek4

First 15 Rhonda numbers in base 26:
In base 10:  7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26:   bde  dke  dme   gd6  16kd  1f6d  1pgd  2e6d  2i2d  2kmd  3ecd  43ed  45kd   64md   7die

First 15 Rhonda numbers in base 27:
In base 10:  4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27:   6fi   g6i   gf9   i2o   k9i   o9b  169k  19ni  1aii  29jf  2i9j  2q9i  32ig  337l  339l

First 15 Rhonda numbers in base 28:
In base 10:  3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28:   3qe  7bc  7c8  9ee   e6g   hc7  16lq  17qq  18em  1m67  1mce  273o  28oe  2al6  2bei

First 15 Rhonda numbers in base 30:
In base 10:  3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30:   3ao  3fi  5kf  5s6  6ia  7fc  8ia  8p6  9ca  afq  aj6  as9   bfa   cn5   eef

First 15 Rhonda numbers in base 32:
In base 10:  1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32:   1so  3gg   d6g   fg4   gas   geh   oq2   p4o   s8n  1ebg  1gea  1hoo  1s4s  1vc8  288l

First 15 Rhonda numbers in base 33:
In base 10:  756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33:   mu  6fb  6vb   cmw   mtf   s3m  1lgb  1pbu  1q3m   3lml   6b78   7bfb   8o2b   9btg   9jm8

First 15 Rhonda numbers in base 34:
In base 10:  5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34:   4uh   c8h   dhe   e8h   j6h   w4h   36lh   3ehi   3f4h   3hqo   3jeh   4h6e   6csh   6h28   7hoi

First 15 Rhonda numbers in base 35:
In base 10:  8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35:   6p7  7pq  7u8   f7e   p9e   y7a  17lu  17sa  1bfe  1fl7  1fpl  1j5e  2a7f   2def   2ebk

First 15 Rhonda numbers in base 36:
In base 10:  1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36:    rs  3pc  4di  6bi   8hi   9ks   a9g   c5i   cz9   hrc  13to  14ou  1g9s  1iq9  1lw6

Raku

Find and show the first 15 so as to display the namesake Rhonda number 25662.

use Prime::Factor;

my @factor-sum;

@factor-sum[1000000] = 42; # Sink a large index to make access thread safe 

sub rhonda ($base) {
    (1..∞).hyper.map: { $_ if $base * (@factor-sum[$_] //= .&prime-factors.sum) == [×] .polymod($base xx *) }
}

for (flat 2..16, 17..36).grep: { !.&is-prime }  -> $b {
    put "\nFirst 15 Rhonda numbers to base $b:";
    my @rhonda = rhonda($b)[^15];
    my $ch = @rhonda[*-1].chars max @rhonda[*-1].base($b).chars;
    put "In base 10: " ~ @rhonda».fmt("%{$ch}s").join: ', ';
    put $b.fmt("In base %2d: ") ~ @rhonda».base($b)».fmt("%{$ch}s").join: ', ';
}
Output:
First 15 Rhonda numbers to base 4:
In base 10:      10206,      11935,      12150,      16031,      45030,      94185,     113022,     114415,     191149,     244713,     259753,     374782,     392121,     503773,     649902
In base  4:    2133132,    2322133,    2331312,    3322133,   22333212,  112333221,  123211332,  123323233,  232222231,  323233221,  333122221, 1123133332, 1133232321, 1322333131, 2132222232

First 15 Rhonda numbers to base 6:
In base 10:     855,    1029,    3813,    5577,    7040,    7304,   15104,   19136,   35350,   36992,   41031,   42009,   60368,   65536,   67821
In base  6:    3543,    4433,   25353,   41453,   52332,   53452,  153532,  224332,  431354,  443132,  513543,  522253, 1143252, 1223224, 1241553

First 15 Rhonda numbers to base 8:
In base 10:   1836,   6318,   6622,  10530,  14500,  14739,  17655,  18550,  25398,  25956,  30562,  39215,  39325,  50875,  51429
In base  8:   3454,  14256,  14736,  24442,  34244,  34623,  42367,  44166,  61466,  62544,  73542, 114457, 114635, 143273, 144345

First 15 Rhonda numbers to base 9:
In base 10:  15540,  21054,  25331,  44360,  44660,  44733,  47652,  50560,  54944,  76857,  77142,  83334,  83694,  96448,  97944
In base  9:  23276,  31783,  37665,  66758,  67232,  67323,  72326,  76317,  83328, 126376, 126733, 136273, 136723, 156264, 158316

First 15 Rhonda numbers to base 10:
In base 10:  1568,  2835,  4752,  5265,  5439,  5664,  5824,  5832,  8526, 12985, 15625, 15698, 19435, 25284, 25662
In base 10:  1568,  2835,  4752,  5265,  5439,  5664,  5824,  5832,  8526, 12985, 15625, 15698, 19435, 25284, 25662

First 15 Rhonda numbers to base 12:
In base 10:   560,   800,  3993,  4425,  4602,  4888,  7315,  8296,  9315, 11849, 12028, 13034, 14828, 15052, 16264
In base 12:   3A8,   568,  2389,  2689,  27B6,  29B4,  4297,  4974,  5483,  6A35,  6B64,  7662,  86B8,  8864,  94B4

First 15 Rhonda numbers to base 14:
In base 10:  11475,  18655,  20565,  29631,  31725,  45387,  58404,  58667,  59950,  63945,  67525,  68904,  91245,  99603, 125543
In base 14:   4279,   6B27,   76CD,   AB27,   B7C1,  1277D,  173DA,  17547,  17BC2,  19437,  1A873,  1B17A,  25377,  28427,  33A75

First 15 Rhonda numbers to base 15:
In base 10:  2392,  2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483
In base 15:   A97,   AEC,  35E8,  4A83,  5269,  5586,  5A1C,  5E39,  735D,  91A8,  936A,  9BA4,  9E1A,  B385,  BA73

First 15 Rhonda numbers to base 16:
In base 10:  1000,  1134,  6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465
In base 16:   3E8,   46E,  1A78,  3E28,  4CA8,  4E4B,  4F83,  5D8A,  66B8,  718E,  7CA2,  7E24,  85BC,  86D9,  8E71

First 15 Rhonda numbers to base 18:
In base 10:  1470,  3000,  8918, 17025, 19402, 20650, 21120, 22156, 26522, 36549, 38354, 43281, 46035, 48768, 54229
In base 18:   49C,   94C,  1998,  2G9F,  35FG,  39D4,  3B36,  3E6G,  49F8,  64E9,  6A6E,  77A9,  7G19,  8696,  956D

First 15 Rhonda numbers to base 20:
In base 10:  1815, 11050, 15295, 21165, 22165, 30702, 34510, 34645, 42292, 44165, 52059, 53416, 65945, 78430, 80712
In base 20:   4AF,  17CA,  1I4F,  2CI5,  2F85,  3GF2,  465A,  46C5,  55EC,  5A85,  6A2J,  6DAG,  84H5,  9G1A,  A1FC

First 15 Rhonda numbers to base 21:
In base 10:  1632,  5390,  8512, 12992, 15678, 25038, 29412, 34017, 39552, 48895, 49147, 61376, 85078, 89590, 91798
In base 21:   3EF,   C4E,   J67,  189E,  1EBC,  2EG6,  33EC,  3E2I,  45E9,  55I7,  5697,  6D3E,  93J7,  9E34,  9J37

First 15 Rhonda numbers to base 22:
In base 10:   2695,   4128,   7865,  28800,  31710,  37030,  71875,  74306, 117760, 117895, 121626, 126002, 131427, 175065, 192753
In base 22:    5CB,    8BE,    G5B,   2FB2,   2LB8,   3AB4,   6GB1,   6LBC,   B16G,   B1CJ,   B96A,   BI78,   C7BL,   G9FB,   I25B

First 15 Rhonda numbers to base 24:
In base 10:  2080,  2709,  3976,  5628,  5656,  7144,  8296,  9030, 10094, 17612, 20559, 24616, 26224, 29106, 31458
In base 24:   3EG,   4GL,   6LG,   9IC,   9JG,   C9G,   E9G,   FG6,   HCE,  16DK,  1BGF,  1IHG,  1LCG,  22CI,  26EI

First 15 Rhonda numbers to base 25:
In base 10:   6764,   9633,  13260,  22022,  53382,  57640,  66015,  69006,  97014, 140130, 142880, 144235, 159724, 162565, 165504
In base 25:    AKE,    FA8,    L5A,   1A5M,   3AA7,   3H5F,   45FF,   4AA6,   655E,   8O55,   93F5,   95JA,   A5DO,   AA2F,   AEK4

First 15 Rhonda numbers to base 26:
In base 10:   7788,   9322,   9374,  11160,  22165,  27885,  34905,  44785,  47385,  49257,  62517,  72709,  74217, 108745, 132302
In base 26:    BDE,    DKE,    DME,    GD6,   16KD,   1F6D,   1PGD,   2E6D,   2I2D,   2KMD,   3ECD,   43ED,   45KD,   64MD,   7DIE

First 15 Rhonda numbers to base 27:
In base 10:  4797, 11844, 12078, 13200, 14841, 17750, 24320, 26883, 27477, 46455, 52750, 58581, 61009, 61446, 61500
In base 27:   6FI,   G6I,   GF9,   I2O,   K9I,   O9B,  169K,  19NI,  1AII,  29JF,  2I9J,  2Q9I,  32IG,  337L,  339L

First 15 Rhonda numbers to base 28:
In base 10:  3094,  5808,  5832,  7462, 11160, 13671, 27270, 28194, 28638, 39375, 39550, 49500, 50862, 52338, 52938
In base 28:   3QE,   7BC,   7C8,   9EE,   E6G,   HC7,  16LQ,  17QQ,  18EM,  1M67,  1MCE,  273O,  28OE,  2AL6,  2BEI

First 15 Rhonda numbers to base 30:
In base 10:  3024,  3168,  5115,  5346,  5950,  6762,  7750,  7956,  8470,  9476,  9576,  9849, 10360, 11495, 13035
In base 30:   3AO,   3FI,   5KF,   5S6,   6IA,   7FC,   8IA,   8P6,   9CA,   AFQ,   AJ6,   AS9,   BFA,   CN5,   EEF

First 15 Rhonda numbers to base 32:
In base 10:  1944,  3600, 13520, 15876, 16732, 16849, 25410, 25752, 28951, 47472, 49610, 50968, 61596, 64904, 74005
In base 32:   1SO,   3GG,   D6G,   FG4,   GAS,   GEH,   OQ2,   P4O,   S8N,  1EBG,  1GEA,  1HOO,  1S4S,  1VC8,  288L

First 15 Rhonda numbers to base 33:
In base 10:    756,   7040,   7568,  13826,  24930,  30613,  59345,  63555,  64372, 131427, 227840, 264044, 313709, 336385, 344858
In base 33:     MU,    6FB,    6VB,    CMW,    MTF,    S3M,   1LGB,   1PBU,   1Q3M,   3LML,   6B78,   7BFB,   8O2B,   9BTG,   9JM8

First 15 Rhonda numbers to base 34:
In base 10:   5661,  14161,  15620,  16473,  22185,  37145, 125579, 134692, 135405, 138472, 140369, 177086, 250665, 255552, 295614
In base 34:    4UH,    C8H,    DHE,    E8H,    J6H,    W4H,   36LH,   3EHI,   3F4H,   3HQO,   3JEH,   4H6E,   6CSH,   6H28,   7HOI

First 15 Rhonda numbers to base 35:
In base 10:   8232,   9476,   9633,  18634,  30954,  41905,  52215,  52440,  56889,  61992,  62146,  66339,  98260, 102180, 103305
In base 35:    6P7,    7PQ,    7U8,    F7E,    P9E,    Y7A,   17LU,   17SA,   1BFE,   1FL7,   1FPL,   1J5E,   2A7F,   2DEF,   2EBK

First 15 Rhonda numbers to base 36:
In base 10:  1000,  4800,  5670,  8190, 10998, 12412, 13300, 15750, 16821, 23016, 51612, 52734, 67744, 70929, 75030
In base 36:    RS,   3PC,   4DI,   6BI,   8HI,   9KS,   A9G,   C5I,   CZ9,   HRC,  13TO,  14OU,  1G9S,  1IQ9,  1LW6

Rust

// [dependencies]
// radix_fmt = "1.0"

fn digit_product(base: u32, mut n: u32) -> u32 {
    let mut product = 1;
    while n != 0 {
        product *= n % base;
        n /= base;
    }
    product
}

fn prime_factor_sum(mut n: u32) -> u32 {
    let mut sum = 0;
    while (n & 1) == 0 {
        sum += 2;
        n >>= 1;
    }
    let mut p = 3;
    while p * p <= n {
        while n % p == 0 {
            sum += p;
            n /= p;
        }
        p += 2;
    }
    if n > 1 {
        sum += n;
    }
    sum
}

fn is_prime(n: u32) -> bool {
    if n < 2 {
        return false;
    }
    if n % 2 == 0 {
        return n == 2;
    }
    if n % 3 == 0 {
        return n == 3;
    }
    let mut p = 5;
    while p * p <= n {
        if n % p == 0 {
            return false;
        }
        p += 2;
        if n % p == 0 {
            return false;
        }
        p += 4;
    }
    true
}

fn is_rhonda(base: u32, n: u32) -> bool {
    digit_product(base, n) == base * prime_factor_sum(n)
}

fn main() {
    let limit = 15;
    for base in 2..=36 {
        if is_prime(base) {
            continue;
        }
        println!("First {} Rhonda numbers to base {}:", limit, base);
        let numbers: Vec<u32> = (1..).filter(|x| is_rhonda(base, *x)).take(limit).collect();
        print!("In base 10:");
        for n in &numbers {
            print!(" {}", n);
        }
        print!("\nIn base {}:", base);
        for n in &numbers {
            print!(" {}", radix_fmt::radix(*n, base as u8));
        }
        print!("\n\n");
    }
}
Output:
First 15 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4

First 15 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75

First 15 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73

First 15 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71

First 15 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d

First 15 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc

First 15 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37

First 15 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b

First 15 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei

First 15 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4

First 15 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die

First 15 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l

First 15 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei

First 15 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef

First 15 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l

First 15 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8

First 15 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi

First 15 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk

First 15 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6

Sidef

func is_rhonda_number(n, base = 10) {
    base.is_composite || return false
    n > 0             || return false
    n.digits(base).prod == base*n.factor.sum
}

for b in (2..16 -> grep { .is_composite }) {
    say ("First 10 Rhonda numbers to base #{b}: ",
        10.by { is_rhonda_number(_, b) })
}
Output:
First 10 Rhonda numbers to base 4: [10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713]
First 10 Rhonda numbers to base 6: [855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992]
First 10 Rhonda numbers to base 8: [1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956]
First 10 Rhonda numbers to base 9: [15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857]
First 10 Rhonda numbers to base 10: [1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985]
First 10 Rhonda numbers to base 12: [560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849]
First 10 Rhonda numbers to base 14: [11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945]
First 10 Rhonda numbers to base 15: [2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758]
First 10 Rhonda numbers to base 16: [1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070]

Swift

func digitProduct(base: Int, num: Int) -> Int {
    var product = 1
    var n = num
    while n != 0 {
        product *= n % base
        n /= base
    }
    return product
}

func primeFactorSum(_ num: Int) -> Int {
    var sum = 0
    var n = num
    while (n & 1) == 0 {
        sum += 2
        n >>= 1
    }
    var p = 3
    while p * p <= n {
        while n % p == 0 {
            sum += p
            n /= p
        }
        p += 2
    }
    if n > 1 {
        sum += n
    }
    return sum
}

func isPrime(_ n: Int) -> Bool {
    if n < 2 {
        return false
    }
    if n % 2 == 0 {
        return n == 2
    }
    if n % 3 == 0 {
        return n == 3
    }
    var p = 5
    while p * p <= n {
        if n % p == 0 {
            return false
        }
        p += 2
        if n % p == 0 {
            return false
        }
        p += 4
    }
    return true
}

func isRhonda(base: Int, num: Int) -> Bool {
    return digitProduct(base: base, num: num) == base * primeFactorSum(num)
}

let limit = 15
for base in 2...36 {
    if isPrime(base) {
        continue
    }
    print("First \(limit) Rhonda numbers to base \(base):")
    let numbers = Array((1...).lazy.filter{ isRhonda(base: base, num: $0) }.prefix(limit))
    print("In base 10:", terminator: "")
    for n in numbers {
        print(" \(n)", terminator: "")
    }
    print("\nIn base \(base):", terminator: "")
    for n in numbers {
        print(" \(String(n, radix: base))", terminator: "")
    }
    print("\n")
}
Output:
First 15 Rhonda numbers to base 4:
In base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713 259753 374782 392121 503773 649902
In base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221 333122221 1123133332 1133232321 1322333131 2132222232

First 15 Rhonda numbers to base 6:
In base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992 41031 42009 60368 65536 67821
In base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132 513543 522253 1143252 1223224 1241553

First 15 Rhonda numbers to base 8:
In base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956 30562 39215 39325 50875 51429
In base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544 73542 114457 114635 143273 144345

First 15 Rhonda numbers to base 9:
In base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857 77142 83334 83694 96448 97944
In base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376 126733 136273 136723 156264 158316

First 15 Rhonda numbers to base 10:
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662
In base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985 15625 15698 19435 25284 25662

First 15 Rhonda numbers to base 12:
In base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849 12028 13034 14828 15052 16264
In base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35 6b64 7662 86b8 8864 94b4

First 15 Rhonda numbers to base 14:
In base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945 67525 68904 91245 99603 125543
In base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437 1a873 1b17a 25377 28427 33a75

First 15 Rhonda numbers to base 15:
In base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758 31150 33004 33550 37925 39483
In base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8 936a 9ba4 9e1a b385 ba73

First 15 Rhonda numbers to base 16:
In base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070 31906 32292 34236 34521 36465
In base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e 7ca2 7e24 85bc 86d9 8e71

First 15 Rhonda numbers to base 18:
In base 10: 1470 3000 8918 17025 19402 20650 21120 22156 26522 36549 38354 43281 46035 48768 54229
In base 18: 49c 94c 1998 2g9f 35fg 39d4 3b36 3e6g 49f8 64e9 6a6e 77a9 7g19 8696 956d

First 15 Rhonda numbers to base 20:
In base 10: 1815 11050 15295 21165 22165 30702 34510 34645 42292 44165 52059 53416 65945 78430 80712
In base 20: 4af 17ca 1i4f 2ci5 2f85 3gf2 465a 46c5 55ec 5a85 6a2j 6dag 84h5 9g1a a1fc

First 15 Rhonda numbers to base 21:
In base 10: 1632 5390 8512 12992 15678 25038 29412 34017 39552 48895 49147 61376 85078 89590 91798
In base 21: 3ef c4e j67 189e 1ebc 2eg6 33ec 3e2i 45e9 55i7 5697 6d3e 93j7 9e34 9j37

First 15 Rhonda numbers to base 22:
In base 10: 2695 4128 7865 28800 31710 37030 71875 74306 117760 117895 121626 126002 131427 175065 192753
In base 22: 5cb 8be g5b 2fb2 2lb8 3ab4 6gb1 6lbc b16g b1cj b96a bi78 c7bl g9fb i25b

First 15 Rhonda numbers to base 24:
In base 10: 2080 2709 3976 5628 5656 7144 8296 9030 10094 17612 20559 24616 26224 29106 31458
In base 24: 3eg 4gl 6lg 9ic 9jg c9g e9g fg6 hce 16dk 1bgf 1ihg 1lcg 22ci 26ei

First 15 Rhonda numbers to base 25:
In base 10: 6764 9633 13260 22022 53382 57640 66015 69006 97014 140130 142880 144235 159724 162565 165504
In base 25: ake fa8 l5a 1a5m 3aa7 3h5f 45ff 4aa6 655e 8o55 93f5 95ja a5do aa2f aek4

First 15 Rhonda numbers to base 26:
In base 10: 7788 9322 9374 11160 22165 27885 34905 44785 47385 49257 62517 72709 74217 108745 132302
In base 26: bde dke dme gd6 16kd 1f6d 1pgd 2e6d 2i2d 2kmd 3ecd 43ed 45kd 64md 7die

First 15 Rhonda numbers to base 27:
In base 10: 4797 11844 12078 13200 14841 17750 24320 26883 27477 46455 52750 58581 61009 61446 61500
In base 27: 6fi g6i gf9 i2o k9i o9b 169k 19ni 1aii 29jf 2i9j 2q9i 32ig 337l 339l

First 15 Rhonda numbers to base 28:
In base 10: 3094 5808 5832 7462 11160 13671 27270 28194 28638 39375 39550 49500 50862 52338 52938
In base 28: 3qe 7bc 7c8 9ee e6g hc7 16lq 17qq 18em 1m67 1mce 273o 28oe 2al6 2bei

First 15 Rhonda numbers to base 30:
In base 10: 3024 3168 5115 5346 5950 6762 7750 7956 8470 9476 9576 9849 10360 11495 13035
In base 30: 3ao 3fi 5kf 5s6 6ia 7fc 8ia 8p6 9ca afq aj6 as9 bfa cn5 eef

First 15 Rhonda numbers to base 32:
In base 10: 1944 3600 13520 15876 16732 16849 25410 25752 28951 47472 49610 50968 61596 64904 74005
In base 32: 1so 3gg d6g fg4 gas geh oq2 p4o s8n 1ebg 1gea 1hoo 1s4s 1vc8 288l

First 15 Rhonda numbers to base 33:
In base 10: 756 7040 7568 13826 24930 30613 59345 63555 64372 131427 227840 264044 313709 336385 344858
In base 33: mu 6fb 6vb cmw mtf s3m 1lgb 1pbu 1q3m 3lml 6b78 7bfb 8o2b 9btg 9jm8

First 15 Rhonda numbers to base 34:
In base 10: 5661 14161 15620 16473 22185 37145 125579 134692 135405 138472 140369 177086 250665 255552 295614
In base 34: 4uh c8h dhe e8h j6h w4h 36lh 3ehi 3f4h 3hqo 3jeh 4h6e 6csh 6h28 7hoi

First 15 Rhonda numbers to base 35:
In base 10: 8232 9476 9633 18634 30954 41905 52215 52440 56889 61992 62146 66339 98260 102180 103305
In base 35: 6p7 7pq 7u8 f7e p9e y7a 17lu 17sa 1bfe 1fl7 1fpl 1j5e 2a7f 2def 2ebk

First 15 Rhonda numbers to base 36:
In base 10: 1000 4800 5670 8190 10998 12412 13300 15750 16821 23016 51612 52734 67744 70929 75030
In base 36: rs 3pc 4di 6bi 8hi 9ks a9g c5i cz9 hrc 13to 14ou 1g9s 1iq9 1lw6

Wren

Library: Wren-math
Library: Wren-fmt
import "./math" for Math, Int, Nums
import "./fmt" for Fmt, Conv

for (b in 2..36) {
    if (Int.isPrime(b)) continue
    var count = 0
    var rhonda = []
    var n = 1
    while (count < 15) {
        var digits = Int.digits(n, b)
        if (!digits.contains(0)) {
            if (b != 10 || (digits.contains(5) && digits.any { |d| d % 2 == 0 })) {
                var calc1 = Nums.prod(digits)
                var calc2 = b * Nums.sum(Int.primeFactors(n))
                if (calc1 == calc2) {
                    rhonda.add(n)
                    count = count + 1
                }
            }
        }
        n = n + 1
    }
    if (rhonda.count > 0) {
        System.print("\nFirst 15 Rhonda numbers in base %(b):")
        var rhonda2 = rhonda.map { |r| r.toString }.toList
        var rhonda3 = rhonda.map { |r| Conv.Itoa(r, b) }.toList
        var maxLen2 = Nums.max(rhonda2.map { |r| r.count })
        var maxLen3 = Nums.max(rhonda3.map { |r| r.count })
        var maxLen  = Math.max(maxLen2, maxLen3) + 1
        Fmt.print("In base 10:  $*s", maxLen, rhonda2)
        Fmt.print("In base $-2d:  $*s", b, maxLen, rhonda3)
    }
}
Output:
First 15 Rhonda numbers in base 4:
In base 10:        10206       11935       12150       16031       45030       94185      113022      114415      191149      244713      259753      374782      392121      503773      649902
In base 4 :      2133132     2322133     2331312     3322133    22333212   112333221   123211332   123323233   232222231   323233221   333122221  1123133332  1133232321  1322333131  2132222232

First 15 Rhonda numbers in base 6:
In base 10:       855     1029     3813     5577     7040     7304    15104    19136    35350    36992    41031    42009    60368    65536    67821
In base 6 :      3543     4433    25353    41453    52332    53452   153532   224332   431354   443132   513543   522253  1143252  1223224  1241553

First 15 Rhonda numbers in base 8:
In base 10:     1836    6318    6622   10530   14500   14739   17655   18550   25398   25956   30562   39215   39325   50875   51429
In base 8 :     3454   14256   14736   24442   34244   34623   42367   44166   61466   62544   73542  114457  114635  143273  144345

First 15 Rhonda numbers in base 9:
In base 10:    15540   21054   25331   44360   44660   44733   47652   50560   54944   76857   77142   83334   83694   96448   97944
In base 9 :    23276   31783   37665   66758   67232   67323   72326   76317   83328  126376  126733  136273  136723  156264  158316

First 15 Rhonda numbers in base 10:
In base 10:    1568   2835   4752   5265   5439   5664   5824   5832   8526  12985  15625  15698  19435  25284  25662
In base 10:    1568   2835   4752   5265   5439   5664   5824   5832   8526  12985  15625  15698  19435  25284  25662

First 15 Rhonda numbers in base 12:
In base 10:     560    800   3993   4425   4602   4888   7315   8296   9315  11849  12028  13034  14828  15052  16264
In base 12:     3A8    568   2389   2689   27B6   29B4   4297   4974   5483   6A35   6B64   7662   86B8   8864   94B4

First 15 Rhonda numbers in base 14:
In base 10:    11475   18655   20565   29631   31725   45387   58404   58667   59950   63945   67525   68904   91245   99603  125543
In base 14:     4279    6B27    76CD    AB27    B7C1   1277D   173DA   17547   17BC2   19437   1A873   1B17A   25377   28427   33A75

First 15 Rhonda numbers in base 15:
In base 10:    2392   2472  11468  15873  17424  18126  19152  20079  24388  30758  31150  33004  33550  37925  39483
In base 15:     A97    AEC   35E8   4A83   5269   5586   5A1C   5E39   735D   91A8   936A   9BA4   9E1A   B385   BA73

First 15 Rhonda numbers in base 16:
In base 10:    1000   1134   6776  15912  19624  20043  20355  23946  26296  29070  31906  32292  34236  34521  36465
In base 16:     3E8    46E   1A78   3E28   4CA8   4E4B   4F83   5D8A   66B8   718E   7CA2   7E24   85BC   86D9   8E71

First 15 Rhonda numbers in base 18:
In base 10:    1470   3000   8918  17025  19402  20650  21120  22156  26522  36549  38354  43281  46035  48768  54229
In base 18:     49C    94C   1998   2G9F   35FG   39D4   3B36   3E6G   49F8   64E9   6A6E   77A9   7G19   8696   956D

First 15 Rhonda numbers in base 20:
In base 10:    1815  11050  15295  21165  22165  30702  34510  34645  42292  44165  52059  53416  65945  78430  80712
In base 20:     4AF   17CA   1I4F   2CI5   2F85   3GF2   465A   46C5   55EC   5A85   6A2J   6DAG   84H5   9G1A   A1FC

First 15 Rhonda numbers in base 21:
In base 10:    1632   5390   8512  12992  15678  25038  29412  34017  39552  48895  49147  61376  85078  89590  91798
In base 21:     3EF    C4E    J67   189E   1EBC   2EG6   33EC   3E2I   45E9   55I7   5697   6D3E   93J7   9E34   9J37

First 15 Rhonda numbers in base 22:
In base 10:     2695    4128    7865   28800   31710   37030   71875   74306  117760  117895  121626  126002  131427  175065  192753
In base 22:      5CB     8BE     G5B    2FB2    2LB8    3AB4    6GB1    6LBC    B16G    B1CJ    B96A    BI78    C7BL    G9FB    I25B

First 15 Rhonda numbers in base 24:
In base 10:    2080   2709   3976   5628   5656   7144   8296   9030  10094  17612  20559  24616  26224  29106  31458
In base 24:     3EG    4GL    6LG    9IC    9JG    C9G    E9G    FG6    HCE   16DK   1BGF   1IHG   1LCG   22CI   26EI

First 15 Rhonda numbers in base 25:
In base 10:     6764    9633   13260   22022   53382   57640   66015   69006   97014  140130  142880  144235  159724  162565  165504
In base 25:      AKE     FA8     L5A    1A5M    3AA7    3H5F    45FF    4AA6    655E    8O55    93F5    95JA    A5DO    AA2F    AEK4

First 15 Rhonda numbers in base 26:
In base 10:     7788    9322    9374   11160   22165   27885   34905   44785   47385   49257   62517   72709   74217  108745  132302
In base 26:      BDE     DKE     DME     GD6    16KD    1F6D    1PGD    2E6D    2I2D    2KMD    3ECD    43ED    45KD    64MD    7DIE

First 15 Rhonda numbers in base 27:
In base 10:    4797  11844  12078  13200  14841  17750  24320  26883  27477  46455  52750  58581  61009  61446  61500
In base 27:     6FI    G6I    GF9    I2O    K9I    O9B   169K   19NI   1AII   29JF   2I9J   2Q9I   32IG   337L   339L

First 15 Rhonda numbers in base 28:
In base 10:    3094   5808   5832   7462  11160  13671  27270  28194  28638  39375  39550  49500  50862  52338  52938
In base 28:     3QE    7BC    7C8    9EE    E6G    HC7   16LQ   17QQ   18EM   1M67   1MCE   273O   28OE   2AL6   2BEI

First 15 Rhonda numbers in base 30:
In base 10:    3024   3168   5115   5346   5950   6762   7750   7956   8470   9476   9576   9849  10360  11495  13035
In base 30:     3AO    3FI    5KF    5S6    6IA    7FC    8IA    8P6    9CA    AFQ    AJ6    AS9    BFA    CN5    EEF

First 15 Rhonda numbers in base 32:
In base 10:    1944   3600  13520  15876  16732  16849  25410  25752  28951  47472  49610  50968  61596  64904  74005
In base 32:     1SO    3GG    D6G    FG4    GAS    GEH    OQ2    P4O    S8N   1EBG   1GEA   1HOO   1S4S   1VC8   288L

First 15 Rhonda numbers in base 33:
In base 10:      756    7040    7568   13826   24930   30613   59345   63555   64372  131427  227840  264044  313709  336385  344858
In base 33:       MU     6FB     6VB     CMW     MTF     S3M    1LGB    1PBU    1Q3M    3LML    6B78    7BFB    8O2B    9BTG    9JM8

First 15 Rhonda numbers in base 34:
In base 10:     5661   14161   15620   16473   22185   37145  125579  134692  135405  138472  140369  177086  250665  255552  295614
In base 34:      4UH     C8H     DHE     E8H     J6H     W4H    36LH    3EHI    3F4H    3HQO    3JEH    4H6E    6CSH    6H28    7HOI

First 15 Rhonda numbers in base 35:
In base 10:     8232    9476    9633   18634   30954   41905   52215   52440   56889   61992   62146   66339   98260  102180  103305
In base 35:      6P7     7PQ     7U8     F7E     P9E     Y7A    17LU    17SA    1BFE    1FL7    1FPL    1J5E    2A7F    2DEF    2EBK

First 15 Rhonda numbers in base 36:
In base 10:    1000   4800   5670   8190  10998  12412  13300  15750  16821  23016  51612  52734  67744  70929  75030
In base 36:      RS    3PC    4DI    6BI    8HI    9KS    A9G    C5I    CZ9    HRC   13TO   14OU   1G9S   1IQ9   1LW6