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Duffinian numbers

Duffinian numbers
You are encouraged to solve this task according to the task description, using any language you may know.

A Duffinian number is a composite number k that is relatively prime to its sigma sum σ.

The sigma sum of k is the sum of the divisors of k.

E.G.

161 is a Duffinian number.

• It is composite. (7 × 23)
• The sigma sum 192 (1 + 7 + 23 + 161) is relatively prime to 161.

Duffinian numbers are very common.

It is not uncommon for two consecutive integers to be Duffinian (a Duffinian twin) (8, 9), (35, 36), (49, 50), etc.

Less common are Duffinian triplets; three consecutive Duffinian numbers. (63, 64, 65), (323, 324, 325), etc.

Much, much less common are Duffinian quadruplets and quintuplets. The first Duffinian quintuplet is (202605639573839041, 202605639573839042, 202605639573839043, 202605639573839044, 202605639573839045).

It is not possible to have six consecutive Duffinian numbers

• Find and show the first 50 Duffinian numbers.
• Find and show at least the first 15 Duffinian triplets.

ALGOL 68

Constructs a table of divisor counts without doing any divisions.

`BEGIN # find Duffinian numbers: non-primes relatively prime to their divisor count #    INT max number            := 500 000;      # largest number we will consider   #    # iterative Greatest Common Divisor routine, returns the gcd of m and n        #    PROC gcd = ( INT m, n )INT:         BEGIN            INT a := ABS m, b := ABS n;            WHILE b /= 0 DO                INT new a = b;                b        := a MOD b;                a        := new a            OD;            a         END # gcd # ;    # construct a table of the divisor counts                                      #    [ 1 : max number ]INT ds; FOR i TO UPB ds DO ds[ i ] := 1 OD;    FOR i FROM 2 TO UPB ds        DO FOR j FROM i BY i TO UPB ds DO ds[ j ] +:= i OD    OD;    # set the divisor counts of non-Duffinian numbers to 0                         #    ds[ 1 ] := 0;  # 1 is not Duffinian                                            #    FOR n FROM 2 TO UPB ds DO        IF INT nds = ds[ n ];           IF nds = n + 1 THEN TRUE ELSE gcd( n, nds ) /= 1 FI        THEN            # n is prime or is not relatively prime to its divisor sum             #            ds[ n ] := 0        FI    OD;    # show the first 50 Duffinian numbers                                          #    print( ( "The first 50 Duffinian numbers:", newline ) );    INT dcount := 0;    FOR n WHILE dcount < 50 DO        IF ds[ n ] /= 0        THEN # found a Duffinian number                                            #            print( ( " ", whole( n, -3) ) );            IF ( dcount +:= 1 ) MOD 25 = 0 THEN print( ( newline ) ) FI        FI    OD;    print( ( newline ) );    # show the duffinian triplets below UPB ds                                     #    print( ( "The Duffinian triplets up to ", whole( UPB ds, 0 ), ":", newline ) );    dcount := 0;    FOR n FROM 3 TO UPB ds DO        IF ds[ n - 2 ] /= 0 AND ds[ n - 1 ] /= 0 AND ds[ n ] /= 0        THEN # found a Duffinian triplet                                           #            print( ( " (", whole( n - 2, -7 ), " ", whole( n - 1, -7 ), " ", whole( n, -7 ), ")" ) );            IF ( dcount +:= 1 ) MOD 4 = 0 THEN print( ( newline ) ) FI        FI    ODEND`
Output:
```The first 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36  39  49  50  55  57  63  64  65  75  77  81  85  93  98 100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217

The Duffinian triplets up to 500000:
(     63      64      65) (    323     324     325) (    511     512     513) (    721     722     723)
(    899     900     901) (   1443    1444    1445) (   2303    2304    2305) (   2449    2450    2451)
(   3599    3600    3601) (   3871    3872    3873) (   5183    5184    5185) (   5617    5618    5619)
(   6049    6050    6051) (   6399    6400    6401) (   8449    8450    8451) (  10081   10082   10083)
(  10403   10404   10405) (  11663   11664   11665) (  12481   12482   12483) (  13447   13448   13449)
(  13777   13778   13779) (  15841   15842   15843) (  17423   17424   17425) (  19043   19044   19045)
(  26911   26912   26913) (  30275   30276   30277) (  36863   36864   36865) (  42631   42632   42633)
(  46655   46656   46657) (  47523   47524   47525) (  53137   53138   53139) (  58563   58564   58565)
(  72961   72962   72963) (  76175   76176   76177) (  79523   79524   79525) (  84099   84100   84101)
(  86527   86528   86529) (  94177   94178   94179) ( 108899  108900  108901) ( 121103  121104  121105)
( 125315  125316  125317) ( 128017  128018  128019) ( 129599  129600  129601) ( 137287  137288  137289)
( 144399  144400  144401) ( 144721  144722  144723) ( 154567  154568  154569) ( 158403  158404  158405)
( 166463  166464  166465) ( 167041  167042  167043) ( 175231  175232  175233) ( 177607  177608  177609)
( 181475  181476  181477) ( 186623  186624  186625) ( 188497  188498  188499) ( 197191  197192  197193)
( 199711  199712  199713) ( 202499  202500  202501) ( 211249  211250  211251) ( 230399  230400  230401)
( 231199  231200  231201) ( 232561  232562  232563) ( 236195  236196  236197) ( 242063  242064  242065)
( 243601  243602  243603) ( 248003  248004  248005) ( 260099  260100  260101) ( 260641  260642  260643)
( 272483  272484  272485) ( 274575  274576  274577) ( 285155  285156  285157) ( 291599  291600  291601)
( 293763  293764  293765) ( 300303  300304  300305) ( 301087  301088  301089) ( 318095  318096  318097)
( 344449  344450  344451) ( 354481  354482  354483) ( 359551  359552  359553) ( 359999  360000  360001)
( 367235  367236  367237) ( 374543  374544  374545) ( 403201  403202  403203) ( 406801  406802  406803)
( 417697  417698  417699) ( 419903  419904  419905) ( 423199  423200  423201) ( 435599  435600  435601)
( 468511  468512  468513) ( 470449  470450  470451) ( 488071  488072  488073)
```

AppleScript

As is often the case with these tasks, it takes as much code to format the output as it does to get the numbers.  :)

`on aliquotSum(n)    if (n < 2) then return 0    set sum to 1    set sqrt to n ^ 0.5    set limit to sqrt div 1    if (limit = sqrt) then        set sum to sum + limit        set limit to limit - 1    end if    repeat with i from 2 to limit        if (n mod i is 0) then set sum to sum + i + n div i    end repeat     return sumend aliquotSum on hcf(a, b)    repeat until (b = 0)        set x to a        set a to b        set b to x mod b    end repeat     if (a < 0) then return -a    return aend hcf on isDuffinian(n)    set aliquot to aliquotSum(n) -- = sigma sum - n. = 1 if n's prime.    return ((aliquot > 1) and (hcf(n, aliquot + n) = 1))end isDuffinian -- Task code:on matrixToText(matrix, w)    script o        property matrix : missing value        property row : missing value    end script     set o's matrix to matrix    set padding to "          "    repeat with r from 1 to (count o's matrix)        set o's row to o's matrix's item r        repeat with i from 1 to (count o's row)            set o's row's item i to text -w thru end of (padding & o's row's item i)        end repeat        set o's matrix's item r to join(o's row, "")    end repeat     return join(o's matrix, linefeed)end matrixToText on join(lst, delim)    set astid to AppleScript's text item delimiters    set AppleScript's text item delimiters to delim    set txt to lst as text    set AppleScript's text item delimiters to astid    return txtend join on task(duffTarget, tupTarget, tupSize)    if ((duffTarget < 1) or (tupTarget < 1) or (tupSize < 2)) then error "Duff parameter(s)."    script o        property duffinians : {}        property tuplets : {}    end script     -- Populate o's duffinians and tuplets lists.    set n to 1    set tuplet to {}    repeat while (((count o's tuplets) < tupTarget) or ((count o's duffinians) < duffTarget))        if (isDuffinian(n)) then            if ((count o's duffinians) < duffTarget) then set end of o's duffinians to n            if (tuplet ends with n - 1) then                set end of tuplet to n            else                if ((count tuplet) = tupSize) then set end of o's tuplets to tuplet                set tuplet to {n}            end if        end if        set n to n + 1    end repeat     -- Format for output.    set duffinians to {}    repeat with i from 1 to duffTarget by 20        set j to i + 19        if (j > duffTarget) then set j to duffTarget        set end of duffinians to items i thru j of o's duffinians    end repeat    set part1 to "First " & duffTarget & " Duffinian numbers:" & linefeed & ¬        matrixToText(duffinians, (count (end of o's duffinians as text)) + 2)    set tupletTypes to {missing value, "twins", "triplets:", "quadruplets:", "quintuplets:"}    set part2 to "First " & tupTarget & " Duffinian " & item tupSize of tupletTypes & linefeed & ¬        matrixToText(o's tuplets, (count (end of end of o's tuplets as text)) + 2)     return part1 & (linefeed & linefeed & part2)end task return task(50, 20, 3) -- First 50 Duffinians, first 20 3-item tuplets.`
Output:
`"First 50 Duffinian numbers:    4    8    9   16   21   25   27   32   35   36   39   49   50   55   57   63   64   65   75   77   81   85   93   98  100  111  115  119  121  125  128  129  133  143  144  155  161  169  171  175  183  185  187  189  201  203  205  209  215  217 First 20 Duffinian triplets:     63     64     65    323    324    325    511    512    513    721    722    723    899    900    901   1443   1444   1445   2303   2304   2305   2449   2450   2451   3599   3600   3601   3871   3872   3873   5183   5184   5185   5617   5618   5619   6049   6050   6051   6399   6400   6401   8449   8450   8451  10081  10082  10083  10403  10404  10405  11663  11664  11665  12481  12482  12483  13447  13448  13449"`

Arturo

`duffinian?: function [n]->    and? [not? prime? n]         [             fn: factors n             [1] = intersection factors sum fn fn         ] first50: new []i: 0while [50 > size first50][    if duffinian? i -> 'first50 ++ i    i: i + 1] print "The first 50 Duffinian numbers:"loop split.every: 10 first50 'row [    print map to [:string] row 'item -> pad item 3] first15: new []i: 0while [15 > size first15][    if every? i..i+2 => duffinian? [        'first15 ++ @[@[i, i+1, i+2]]        i: i+2    ]    i: i + 1] print ""print "The first 15 Duffinian triplets:"loop split.every: 5 first15 'row [    print map row 'item -> pad.right as.code item 17]`
Output:
```The first 50 Duffinian numbers:
1   4   8   9  16  21  25  27  32  35
36  39  49  50  55  57  63  64  65  75
77  81  85  93  98 100 111 115 119 121
125 128 129 133 143 144 155 161 169 171
175 183 185 187 189 201 203 205 209 215

The first 15 Duffinian triplets:
[63 64 65]        [323 324 325]     [511 512 513]     [721 722 723]     [899 900 901]
[1443 1444 1445]  [2303 2304 2305]  [2449 2450 2451]  [3599 3600 3601]  [3871 3872 3873]
[5183 5184 5185]  [5617 5618 5619]  [6049 6050 6051]  [6399 6400 6401]  [8449 8450 8451]```

C++

`#include <iomanip>#include <iostream>#include <numeric>#include <sstream> bool duffinian(int n) {    if (n == 2)        return false;    int total = 1, power = 2, m = n;    for (; (n & 1) == 0; power <<= 1, n >>= 1)        total += power;    for (int p = 3; p * p <= n; p += 2) {        int sum = 1;        for (power = p; n % p == 0; power *= p, n /= p)            sum += power;        total *= sum;    }    if (m == n)        return false;    if (n > 1)        total *= n + 1;    return std::gcd(total, m) == 1;} int main() {    std::cout << "First 50 Duffinian numbers:\n";    for (int n = 1, count = 0; count < 50; ++n) {        if (duffinian(n))            std::cout << std::setw(3) << n << (++count % 10 == 0 ? '\n' : ' ');    }    std::cout << "\nFirst 50 Duffinian triplets:\n";    for (int n = 1, m = 0, count = 0; count < 50; ++n) {        if (duffinian(n))            ++m;        else            m = 0;        if (m == 3) {            std::ostringstream os;            os << '(' << n - 2 << ", " << n - 1 << ", " << n << ')';            std::cout << std::left << std::setw(24) << os.str()                      << (++count % 3 == 0 ? '\n' : ' ');        }    }    std::cout << '\n';}`
Output:
```First 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36
39  49  50  55  57  63  64  65  75  77
81  85  93  98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

First 50 Duffinian triplets:
(63, 64, 65)             (323, 324, 325)          (511, 512, 513)
(721, 722, 723)          (899, 900, 901)          (1443, 1444, 1445)
(2303, 2304, 2305)       (2449, 2450, 2451)       (3599, 3600, 3601)
(3871, 3872, 3873)       (5183, 5184, 5185)       (5617, 5618, 5619)
(6049, 6050, 6051)       (6399, 6400, 6401)       (8449, 8450, 8451)
(10081, 10082, 10083)    (10403, 10404, 10405)    (11663, 11664, 11665)
(12481, 12482, 12483)    (13447, 13448, 13449)    (13777, 13778, 13779)
(15841, 15842, 15843)    (17423, 17424, 17425)    (19043, 19044, 19045)
(26911, 26912, 26913)    (30275, 30276, 30277)    (36863, 36864, 36865)
(42631, 42632, 42633)    (46655, 46656, 46657)    (47523, 47524, 47525)
(53137, 53138, 53139)    (58563, 58564, 58565)    (72961, 72962, 72963)
(76175, 76176, 76177)    (79523, 79524, 79525)    (84099, 84100, 84101)
(86527, 86528, 86529)    (94177, 94178, 94179)    (108899, 108900, 108901)
(121103, 121104, 121105) (125315, 125316, 125317) (128017, 128018, 128019)
(129599, 129600, 129601) (137287, 137288, 137289) (144399, 144400, 144401)
(144721, 144722, 144723) (154567, 154568, 154569) (158403, 158404, 158405)
(166463, 166464, 166465) (167041, 167042, 167043)
```

Factor

Works with: Factor version 0.99 2021-06-02
`USING: combinators.short-circuit.smart grouping io kernel listslists.lazy math math.primes math.primes.factors math.statisticsprettyprint sequences sequences.deep ; : duffinian? ( n -- ? )    { [ prime? not ] [ dup divisors sum simple-gcd 1 = ] } && ; : duffinians ( -- list ) 3 lfrom [ duffinian? ] lfilter ; : triples ( -- list )    duffinians dup cdr dup cdr lzip lzip [ flatten ] lmap-lazy    [ differences { 1 1 } = ] lfilter ; "First 50 Duffinian numbers:" print50 duffinians ltake list>array 10 group simple-table. nl "First 15 Duffinian triplets:" print15 triples ltake list>array simple-table.`
Output:
```First 50 Duffinian numbers:
4   8   9   16  21  25  27  32  35  36
39  49  50  55  57  63  64  65  75  77
81  85  93  98  100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

First 15 Duffinian triplets:
63   64   65
323  324  325
511  512  513
721  722  723
899  900  901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451
```

Go

Translation of: Wren
Library: Go-rcu
`package main import (    "fmt"    "math"    "rcu") func isSquare(n int) bool {    s := int(math.Sqrt(float64(n)))    return s*s == n} func main() {    limit := 200000 // say    d := rcu.PrimeSieve(limit-1, true)    d[1] = false    for i := 2; i < limit; i++ {        if !d[i] {            continue        }        if i%2 == 0 && !isSquare(i) && !isSquare(i/2) {            d[i] = false            continue        }        sigmaSum := rcu.SumInts(rcu.Divisors(i))        if rcu.Gcd(sigmaSum, i) != 1 {            d[i] = false        }    }     var duff []int    for i := 1; i < len(d); i++ {        if d[i] {            duff = append(duff, i)        }    }    fmt.Println("First 50 Duffinian numbers:")    rcu.PrintTable(duff[0:50], 10, 3, false)     var triplets [][3]int    for i := 2; i < limit; i++ {        if d[i] && d[i-1] && d[i-2] {            triplets = append(triplets, [3]int{i - 2, i - 1, i})        }    }    fmt.Println("\nFirst 56 Duffinian triplets:")    for i := 0; i < 14; i++ {        s := fmt.Sprintf("%6v", triplets[i*4:i*4+4])        fmt.Println(s[1 : len(s)-1])    }}`
Output:
```First 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36
39  49  50  55  57  63  64  65  75  77
81  85  93  98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

First 56 Duffinian triplets:
[    63     64     65] [   323    324    325] [   511    512    513] [   721    722    723]
[   899    900    901] [  1443   1444   1445] [  2303   2304   2305] [  2449   2450   2451]
[  3599   3600   3601] [  3871   3872   3873] [  5183   5184   5185] [  5617   5618   5619]
[  6049   6050   6051] [  6399   6400   6401] [  8449   8450   8451] [ 10081  10082  10083]
[ 10403  10404  10405] [ 11663  11664  11665] [ 12481  12482  12483] [ 13447  13448  13449]
[ 13777  13778  13779] [ 15841  15842  15843] [ 17423  17424  17425] [ 19043  19044  19045]
[ 26911  26912  26913] [ 30275  30276  30277] [ 36863  36864  36865] [ 42631  42632  42633]
[ 46655  46656  46657] [ 47523  47524  47525] [ 53137  53138  53139] [ 58563  58564  58565]
[ 72961  72962  72963] [ 76175  76176  76177] [ 79523  79524  79525] [ 84099  84100  84101]
[ 86527  86528  86529] [ 94177  94178  94179] [108899 108900 108901] [121103 121104 121105]
[125315 125316 125317] [128017 128018 128019] [129599 129600 129601] [137287 137288 137289]
[144399 144400 144401] [144721 144722 144723] [154567 154568 154569] [158403 158404 158405]
[166463 166464 166465] [167041 167042 167043] [175231 175232 175233] [177607 177608 177609]
[181475 181476 181477] [186623 186624 186625] [188497 188498 188499] [197191 197192 197193]
```

J

Implementation:

`sigmasum=: >:@#.~/.~&.q:composite=: 1&< * 0 = 1&p: duffinian=: composite * 1 = ] +. sigmasum`

`   5 10\$(#~ duffinian) 1+i.1000  4   8   9  16  21  25  27  32  35  36 39  49  50  55  57  63  64  65  75  77 81  85  93  98 100 111 115 119 121 125128 129 133 143 144 155 161 169 171 175183 185 187 189 201 203 205 209 215 217   (i.3)+/~15 {.(#~ 1 1 1 E. duffinian) 1+i.100000  63   64   65 323  324  325 511  512  513 721  722  723 899  900  9011443 1444 14452303 2304 23052449 2450 24513599 3600 36013871 3872 38735183 5184 51855617 5618 56196049 6050 60516399 6400 64018449 8450 8451`

Julia

`using Primes function σ(n)    f = [one(n)]    for (p,e) in factor(n)        f = reduce(vcat, [f*p^j for j in 1:e], init=f)    end    return sum(f)end isDuffinian(n) = !isprime(n) && gcd(n, σ(n)) == 1 function testDuffinians()    println("First 50 Duffinian numbers:")    foreach(p -> print(rpad(p[2], 4), p[1] % 25 == 0 ? "\n" : ""),        enumerate(filter(isDuffinian, 2:217)))    n, found = 2, 0    println("\nFifteen Duffinian triplets:")    while found < 15        if isDuffinian(n) && isDuffinian(n + 1) && isDuffinian(n + 2)            println(lpad(n, 6), lpad(n +1, 6), lpad(n + 2, 6))            found += 1        end        n += 1    endend testDuffinians() `
Output:
```First 50 Duffinian numbers:
4   8   9   16  21  25  27  32  35  36  39  49  50  55  57  63  64  65  75  77  81  85  93  98  100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217

Fifteen Duffinian triplets:
63    64    65
323   324   325
511   512   513
721   722   723
899   900   901
1443  1444  1445
2303  2304  2305
2449  2450  2451
3599  3600  3601
3871  3872  3873
5183  5184  5185
5617  5618  5619
6049  6050  6051
6399  6400  6401
8449  8450  8451
```

Perl

Library: ntheory
`use strict;use warnings;use feature <say state>;use List::Util 'max';use ntheory qw<divisor_sum is_prime gcd>; sub table { my \$t = shift() * (my \$c = 1 + max map {length} @_); ( sprintf( ('%'.\$c.'s')x@_, @_) ) =~ s/.{1,\$t}\K/\n/gr } sub duffinian {    my(\$n) = @_;    state \$c = 1; state @D;    do { push @D, \$c if ! is_prime ++\$c and 1 == gcd(\$c,divisor_sum(\$c)) } until @D > \$n;    \$D[\$n];} say "First 50 Duffinian numbers:";say table 10, map { duffinian \$_-1 } 1..50; my(@d3,@triples) = (4, 8, 9); my \$n = 3;while (@triples < 39) {    push @triples, '('.join(', ',@d3).')' if \$d3[1] == 1+\$d3[0] and \$d3[2] == 2+\$d3[0];    shift @d3 and push @d3, duffinian ++\$n;} say 'First 39 Duffinian triplets:';say table 3, @triples;`
Output:
```First 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36
39  49  50  55  57  63  64  65  75  77
81  85  93  98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

First 39 Duffinian triplets:
(63, 64, 65)          (323, 324, 325)          (511, 512, 513)
(721, 722, 723)          (899, 900, 901)       (1443, 1444, 1445)
(2303, 2304, 2305)       (2449, 2450, 2451)       (3599, 3600, 3601)
(3871, 3872, 3873)       (5183, 5184, 5185)       (5617, 5618, 5619)
(6049, 6050, 6051)       (6399, 6400, 6401)       (8449, 8450, 8451)
(10081, 10082, 10083)    (10403, 10404, 10405)    (11663, 11664, 11665)
(12481, 12482, 12483)    (13447, 13448, 13449)    (13777, 13778, 13779)
(15841, 15842, 15843)    (17423, 17424, 17425)    (19043, 19044, 19045)
(26911, 26912, 26913)    (30275, 30276, 30277)    (36863, 36864, 36865)
(42631, 42632, 42633)    (46655, 46656, 46657)    (47523, 47524, 47525)
(53137, 53138, 53139)    (58563, 58564, 58565)    (72961, 72962, 72963)
(76175, 76176, 76177)    (79523, 79524, 79525)    (84099, 84100, 84101)
(86527, 86528, 86529)    (94177, 94178, 94179) (108899, 108900, 108901)```

Phix

```with javascript_semantics
sequence duffinian = {false}
integer n = 2, count = 0, triplet = 0, triple_count = 0
while triple_count<50 do
bool bDuff = not is_prime(n) and gcd(n,sum(factors(n,1)))=1
duffinian &= bDuff
if bDuff then
count += 1
if count=50 then
sequence s50 = apply(true,sprintf,{{"%3d"},find_all(true,duffinian)})
printf(1,"First 50 Duffinian numbers:\n%s\n",join_by(s50,1,25," "))
end if
triplet += 1
triple_count += (triplet>=3)
else
triplet = 0
end if
n += 1
end while
sequence s = apply(true,sq_add,{match_all({true,true,true},duffinian),{{0,1,2}}}),
printf(1,"First 50 Duffinian triplets:\n%s\n",{join_by(p,1,4," ")})
```
Output:
```First 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36  39  49  50  55  57  63  64  65  75  77  81  85  93  98 100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217

First 50 Duffinian triplets:
[63,64,65]               [323,324,325]            [511,512,513]            [721,722,723]
[899,900,901]            [1443,1444,1445]         [2303,2304,2305]         [2449,2450,2451]
[3599,3600,3601]         [3871,3872,3873]         [5183,5184,5185]         [5617,5618,5619]
[6049,6050,6051]         [6399,6400,6401]         [8449,8450,8451]         [10081,10082,10083]
[10403,10404,10405]      [11663,11664,11665]      [12481,12482,12483]      [13447,13448,13449]
[13777,13778,13779]      [15841,15842,15843]      [17423,17424,17425]      [19043,19044,19045]
[26911,26912,26913]      [30275,30276,30277]      [36863,36864,36865]      [42631,42632,42633]
[46655,46656,46657]      [47523,47524,47525]      [53137,53138,53139]      [58563,58564,58565]
[72961,72962,72963]      [76175,76176,76177]      [79523,79524,79525]      [84099,84100,84101]
[86527,86528,86529]      [94177,94178,94179]      [108899,108900,108901]   [121103,121104,121105]
[125315,125316,125317]   [128017,128018,128019]   [129599,129600,129601]   [137287,137288,137289]
[144399,144400,144401]   [144721,144722,144723]   [154567,154568,154569]   [158403,158404,158405]
[166463,166464,166465]   [167041,167042,167043]
```

Raku

`use Prime::Factor; my @duffinians = lazy (3..*).hyper.grep: { !.is-prime && \$_ gcd .&divisors.sum == 1 }; put "First 50 Duffinian numbers:\n" ~@duffinians[^50].batch(10)».fmt("%3d").join: "\n"; put "\nFirst 40 Duffinian triplets:\n" ~    ((^∞).grep: -> \$n { (@duffinians[\$n] + 1 == @duffinians[\$n + 1]) && (@duffinians[\$n] + 2 == @duffinians[\$n + 2]) })[^40]\    .map( { "({@duffinians[\$_ .. \$_+2].join: ', '})" } ).batch(4)».fmt("%-24s").join: "\n";`
Output:
```First 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36
39  49  50  55  57  63  64  65  75  77
81  85  93  98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

First 40 Duffinian triplets:
(63, 64, 65)             (323, 324, 325)          (511, 512, 513)          (721, 722, 723)
(899, 900, 901)          (1443, 1444, 1445)       (2303, 2304, 2305)       (2449, 2450, 2451)
(3599, 3600, 3601)       (3871, 3872, 3873)       (5183, 5184, 5185)       (5617, 5618, 5619)
(6049, 6050, 6051)       (6399, 6400, 6401)       (8449, 8450, 8451)       (10081, 10082, 10083)
(10403, 10404, 10405)    (11663, 11664, 11665)    (12481, 12482, 12483)    (13447, 13448, 13449)
(13777, 13778, 13779)    (15841, 15842, 15843)    (17423, 17424, 17425)    (19043, 19044, 19045)
(26911, 26912, 26913)    (30275, 30276, 30277)    (36863, 36864, 36865)    (42631, 42632, 42633)
(46655, 46656, 46657)    (47523, 47524, 47525)    (53137, 53138, 53139)    (58563, 58564, 58565)
(72961, 72962, 72963)    (76175, 76176, 76177)    (79523, 79524, 79525)    (84099, 84100, 84101)
(86527, 86528, 86529)    (94177, 94178, 94179)    (108899, 108900, 108901) (121103, 121104, 121105)```

Sidef

`func is_duffinian(n) {    n.is_composite && n.is_coprime(n.sigma)} say "First 50 Duffinian numbers:"say 50.by(is_duffinian) say "\nFirst 15 Duffinian triplets:"15.by{|n| ^3 -> all {|k| is_duffinian(n+k) } }.each {|n|    printf("(%s, %s, %s)\n", n, n+1, n+2)}`
Output:
```First 50 Duffinian numbers:
[4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, 64, 65, 75, 77, 81, 85, 93, 98, 100, 111, 115, 119, 121, 125, 128, 129, 133, 143, 144, 155, 161, 169, 171, 175, 183, 185, 187, 189, 201, 203, 205, 209, 215, 217]

First 15 Duffinian triplets:
(63, 64, 65)
(323, 324, 325)
(511, 512, 513)
(721, 722, 723)
(899, 900, 901)
(1443, 1444, 1445)
(2303, 2304, 2305)
(2449, 2450, 2451)
(3599, 3600, 3601)
(3871, 3872, 3873)
(5183, 5184, 5185)
(5617, 5618, 5619)
(6049, 6050, 6051)
(6399, 6400, 6401)
(8449, 8450, 8451)
```

Wren

Library: Wren-math
Library: Wren-seq
Library: Wren-fmt
`import "./math" for Int, Numsimport "./seq" for Lstimport "./fmt" for Fmt var limit = 200000  // sayvar d = Int.primeSieve(limit-1, false)d[1] = falsefor (i in 2...limit) {    if (!d[i]) continue    if (i % 2 == 0 && !Int.isSquare(i) && !Int.isSquare(i/2)) {        d[i] = false        continue    }    var sigmaSum = Nums.sum(Int.divisors(i))    if (Int.gcd(sigmaSum, i) != 1) d[i] = false} var duff = (1...d.count).where { |i| d[i] }.toListSystem.print("First 50 Duffinian numbers:")for (chunk in Lst.chunks(duff[0..49], 10)) Fmt.print("\$3d", chunk) var triplets = []for (i in 2...limit) {    if (d[i] && d[i-1] && d[i-2]) triplets.add([i-2, i-1, i])}System.print("\nFirst 50 Duffinian triplets:")for (chunk in Lst.chunks(triplets[0..49], 4)) Fmt.print("\$-25s", chunk)`
Output:
```First 50 Duffinian numbers:
4   8   9  16  21  25  27  32  35  36
39  49  50  55  57  63  64  65  75  77
81  85  93  98 100 111 115 119 121 125
128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

First 50 Duffinian triplets:
[63, 64, 65]              [323, 324, 325]           [511, 512, 513]           [721, 722, 723]
[899, 900, 901]           [1443, 1444, 1445]        [2303, 2304, 2305]        [2449, 2450, 2451]
[3599, 3600, 3601]        [3871, 3872, 3873]        [5183, 5184, 5185]        [5617, 5618, 5619]
[6049, 6050, 6051]        [6399, 6400, 6401]        [8449, 8450, 8451]        [10081, 10082, 10083]
[10403, 10404, 10405]     [11663, 11664, 11665]     [12481, 12482, 12483]     [13447, 13448, 13449]
[13777, 13778, 13779]     [15841, 15842, 15843]     [17423, 17424, 17425]     [19043, 19044, 19045]
[26911, 26912, 26913]     [30275, 30276, 30277]     [36863, 36864, 36865]     [42631, 42632, 42633]
[46655, 46656, 46657]     [47523, 47524, 47525]     [53137, 53138, 53139]     [58563, 58564, 58565]
[72961, 72962, 72963]     [76175, 76176, 76177]     [79523, 79524, 79525]     [84099, 84100, 84101]
[86527, 86528, 86529]     [94177, 94178, 94179]     [108899, 108900, 108901]  [121103, 121104, 121105]
[125315, 125316, 125317]  [128017, 128018, 128019]  [129599, 129600, 129601]  [137287, 137288, 137289]
[144399, 144400, 144401]  [144721, 144722, 144723]  [154567, 154568, 154569]  [158403, 158404, 158405]
[166463, 166464, 166465]  [167041, 167042, 167043]
```

XPL0

`func IsPrime(N);        \Return 'true' if N is primeint  N, I;[if N <= 2 then return N = 2;if (N&1) = 0 then \even >2\ return false;for I:= 3 to sqrt(N) do    [if rem(N/I) = 0 then return false;    I:= I+1;    ];return true;]; func    SumDiv(Num);    \Return sum of proper divisors of Numint     Num, Div, Sum, Quot;[Div:= 2;Sum:= 0;loop    [Quot:= Num/Div;        if Div > Quot then quit;        if rem(0) = 0 then            [Sum:= Sum + Div;            if Div # Quot then Sum:= Sum + Quot;            ];        Div:= Div+1;        ];return Sum+1;]; func GCD(A, B);         \Return greatest common divisor of A and Bint  A, B;[while A#B do  if A>B then A:= A-B         else B:= B-A;return A;]; func Duff(N);           \Return 'true' if N is a Duffinian numberint  N;[if IsPrime(N) then return false;return GCD(SumDiv(N), N) = 1;]; int C, N;[Format(4, 0);C:= 0;  N:= 4;loop    [if Duff(N) then            [RlOut(0, float(N));            C:= C+1;            if C >= 50 then quit;            if rem(C/20) = 0 then CrLf(0);            ];        N:= N+1;        ];CrLf(0);  CrLf(0);Format(5, 0);C:= 0;  N:= 4;loop    [if Duff(N) & Duff(N+1) & Duff(N+2) then            [RlOut(0, float(N));  RlOut(0, float(N+1));  RlOut(0, float(N+2));            CrLf(0);            C:= C+1;            if C >= 15 then quit;            ];        N:= N+1;        ];]`
Output:
```   4   8   9  16  21  25  27  32  35  36  39  49  50  55  57  63  64  65  75  77
81  85  93  98 100 111 115 119 121 125 128 129 133 143 144 155 161 169 171 175
183 185 187 189 201 203 205 209 215 217

63   64   65
323  324  325
511  512  513
721  722  723
899  900  901
1443 1444 1445
2303 2304 2305
2449 2450 2451
3599 3600 3601
3871 3872 3873
5183 5184 5185
5617 5618 5619
6049 6050 6051
6399 6400 6401
8449 8450 8451
```