Smith numbers

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

Smith numbers are numbers such that the sum of the decimal digits of the integers that make up that number is the same as the sum of the decimal digits of its prime factors excluding 1.

By definition, all primes are excluded as they (naturally) satisfy this condition!

Smith numbers are also known as   joke   numbers.


Example

Using the number 166
Find the prime factors of 166 which are: 2 x 83
Then, take those two prime factors and sum all their decimal digits: 2 + 8 + 3 which is 13
Then, take the decimal digits of 166 and add their decimal digits: 1 + 6 + 6 which is 13
Therefore, the number 166 is a Smith number.


Task

Write a program to find all Smith numbers below 10000.


See also



Ada[edit]

Works with: Ada version 2012
 
with Ada.Text_IO;
 
procedure smith is
type Vector is array (natural range <>) of Positive;
empty_vector : constant Vector(1..0):= (others=>1);
 
function digits_sum (n : Positive) return Positive is
(if n < 10 then n else n mod 10 + digits_sum (n / 10));
 
function prime_factors (n : Positive; d : Positive := 2) return Vector is
(if n = 1 then empty_vector elsif n mod d = 0 then prime_factors (n / d, d) & d
else prime_factors (n, d + (if d=2 then 1 else 2)));
 
function vector_digits_sum (v : Vector) return Natural is
(if v'Length = 0 then 0 else digits_sum (v(v'First)) + vector_digits_sum (v(v'First+1..v'Last)));
 
begin
for n in 1..10000 loop
declare
primes : Vector := prime_factors (n);
begin
if primes'Length > 1 and then vector_digits_sum (primes) = digits_sum (n) then
Ada.Text_IO.put (n'img);
end if;
end;
end loop;
end smith;
 

ALGOL 68[edit]

# sieve of Eratosthene: sets s[i] to TRUE if i is prime, FALSE otherwise #
PROC sieve = ( REF[]BOOL s )VOID:
BEGIN
# start with everything flagged as prime #
FOR i TO UPB s DO s[ i ] := TRUE OD;
# sieve out the non-primes #
s[ 1 ] := FALSE;
FOR i FROM 2 TO ENTIER sqrt( UPB s ) DO
IF s[ i ] THEN FOR p FROM i * i BY i TO UPB s DO s[ p ] := FALSE OD FI
OD
END # sieve # ;
 
# construct a sieve of primes up to the maximum number required for the task #
INT max number = 10 000;
[ 1 : max number ]BOOL is prime;
sieve( is prime );
 
# returns the sum of the digits of n #
OP DIGITSUM = ( INT n )INT:
BEGIN
INT sum := 0;
INT rest := ABS n;
WHILE rest > 0 DO
sum +:= rest MOD 10;
rest OVERAB 10
OD;
sum
END # DIGITSUM # ;
 
# returns TRUE if n is a Smith number, FALSE otherwise #
# n must be between 1 and max number #
PROC is smith = ( INT n )BOOL:
IF is prime[ ABS n ] THEN
# primes are not Smith numbers #
FALSE
ELSE
# find the factors of n and sum the digits of the factors #
INT rest := ABS n;
INT factor digit sum := 0;
INT factor := 2;
WHILE factor < max number AND rest > 1 DO
IF NOT is prime[ factor ] THEN
# factor isn't a prime #
factor +:= 1
ELSE
# factor is a prime #
IF rest MOD factor /= 0 THEN
# factor isn't a factor of n #
factor +:= 1
ELSE
# factor is a factor of n #
rest OVERAB factor;
factor digit sum +:= DIGITSUM factor
FI
FI
OD;
( factor digit sum = DIGITSUM n )
FI # is smith # ;
 
# print all the Smith numbers below the maximum required #
INT smith count := 0;
FOR n TO max number - 1 DO
IF is smith( n ) THEN
# have a smith number #
print( ( whole( n, -7 ) ) );
smith count +:= 1;
IF smith count MOD 10 = 0 THEN
print( ( newline ) )
FI
FI
OD;
print( ( newline, "THere are ", whole( smith count, -7 ), " Smith numbers below ", whole( max number, -7 ), newline ) )
 
Output:
      4     22     27     58     85     94    121    166    202    265
    274    319    346    355    378    382    391    438    454    483
    ...
   9717   9735   9742   9760   9778   9840   9843   9849   9861   9880
   9895   9924   9942   9968   9975   9985
THere are     376 Smith numbers below   10000

C[edit]

Translation of: C++
 
#include <stdlib.h>
#include <stdio.h>
#include <stdbool.h>
 
int numPrimeFactors(unsigned x) {
unsigned p = 2;
int pf = 0;
if (x == 1)
return 1;
else {
while (true) {
if (!(x % p)) {
pf++;
x /= p;
if (x == 1)
return pf;
}
else
++p;
}
}
}
 
void primeFactors(unsigned x, unsigned* arr) {
unsigned p = 2;
int pf = 0;
if (x == 1)
arr[pf] = 1;
else {
while (true) {
if (!(x % p)) {
arr[pf++] = p;
x /= p;
if (x == 1)
return;
}
else
p++;
}
}
}
 
unsigned sumDigits(unsigned x) {
unsigned sum = 0, y;
while (x) {
y = x % 10;
sum += y;
x /= 10;
}
return sum;
}
 
unsigned sumFactors(unsigned* arr, int size) {
unsigned sum = 0;
for (int a = 0; a < size; a++)
sum += sumDigits(arr[a]);
return sum;
}
 
void listAllSmithNumbers(unsigned x) {
unsigned *arr;
for (unsigned a = 4; a < x; a++) {
int numfactors = numPrimeFactors(a);
arr = (unsigned*)malloc(numfactors * sizeof(unsigned));
if (numfactors < 2)
continue;
primeFactors(a, arr);
if (sumDigits(a) == sumFactors(arr,numfactors))
printf("%4u ",a);
free(arr);
}
}
 
int main(int argc, char* argv[]) {
printf("All the Smith Numbers < 10000 are:\n");
listAllSmithNumbers(10000);
return 0;
}
 
Output:
All the Smith Numbers < 10000 are:
   4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382
 391  438  454  483  517  526  535  562  576  588  627  634  636  645  648  654
 663  666  690  706  728  729  762  778  825  852  861  895  913  915  922  958 
 985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 
1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 
1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 
2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 
2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 
3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 
3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 
4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 
4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 
5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 
5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 
6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 
6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 
7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 
7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 
8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 
8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 
8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 
9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 
9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 
9861 9880 9895 9924 9942 9968 9975 9985

C++[edit]

 
#include <iostream>
#include <vector>
#include <iomanip>
 
void primeFactors( unsigned n, std::vector<unsigned>& r ) {
int f = 2; if( n == 1 ) r.push_back( 1 );
else {
while( true ) {
if( !( n % f ) ) {
r.push_back( f );
n /= f; if( n == 1 ) return;
}
else f++;
}
}
}
unsigned sumDigits( unsigned n ) {
unsigned sum = 0, m;
while( n ) {
m = n % 10; sum += m;
n -= m; n /= 10;
}
return sum;
}
unsigned sumDigits( std::vector<unsigned>& v ) {
unsigned sum = 0;
for( std::vector<unsigned>::iterator i = v.begin(); i != v.end(); i++ ) {
sum += sumDigits( *i );
}
return sum;
}
void listAllSmithNumbers( unsigned n ) {
std::vector<unsigned> pf;
for( unsigned i = 4; i < n; i++ ) {
primeFactors( i, pf ); if( pf.size() < 2 ) continue;
if( sumDigits( i ) == sumDigits( pf ) )
std::cout << std::setw( 4 ) << i << " ";
pf.clear();
}
std::cout << "\n\n";
}
int main( int argc, char* argv[] ) {
listAllSmithNumbers( 10000 );
return 0;
}
 
Output:
   4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382
 391  438  454  483  517  526  535  562  576  627  634  636  645  663  666  690
...
9301 9330 9346 9355 9382 9386 9387 9396 9427 9483 9535 9571 9598 9633 9634 9639 
9648 9657 9684 9708 9717 9735 9742 9760 9778 9843 9849 9861 9880 9895 9975 9985

Elixir[edit]

defmodule Smith do
def number?(n) do
d = decomposition(n)
length(d)>1 and sum_digits(n) == Enum.map(d, &sum_digits/1) |> Enum.sum
end
 
defp sum_digits(n) do
Integer.digits(n) |> Enum.sum
end
 
defp decomposition(n, k\\2, acc\\[])
defp decomposition(n, k, acc) when n < k*k, do: [n | acc]
defp decomposition(n, k, acc) when rem(n, k) == 0, do: decomposition(div(n, k), k, [k | acc])
defp decomposition(n, k, acc), do: decomposition(n, k+1, acc)
end
 
m = 10000
smith = Enum.filter(1..m, &Smith.number?/1)
IO.puts "#{length(smith)} smith numbers below #{m}:"
IO.puts "First 10: #{Enum.take(smith,10) |> Enum.join(", ")}"
IO.puts "Last 10: #{Enum.take(smith,-10) |> Enum.join(", ")}"
Output:
376 smith numbers below 10000:
First 10: 4, 22, 27, 58, 85, 94, 121, 166, 202, 265
Last  10: 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985

Fortran[edit]

This is F90 style, to take advantage of module PRIMESTUFF from Extensible_prime_generator to get at a supply of prime numbers and related routines, and contains a slightly trimmed module FACTORISE from the FRACTRAN project that factorises a number but which doesn't need the slight extras for the FRACTRAN process. Re-using code is good, but one must watch out for forgotten details that may not fit into the new context: the FRACTRAN project wanted the number of the prime, not the prime number (itself) in its lists of factors, whereas this project wanted the actual prime number in its list of factors. So, it would be PRIME(F.PNUM(i)), because "PNUM" means "the prime's number"... However, acquiring the i'th prime via PRIME(i) is not a matter of array access, it involves a function with some fancy arithmetic. Since the factorisation requires consecutive prime numbers, using NEXTPRIME(F) is a better choice, and the run is much faster since many numbers are being factorised: the FRACTRAN project factorised only a few. So, a change from "PNUM" to "PVAL" with the prime's value stored instead of its index, even though this means that PNUM(0) which holds the number of prime factors becomes PVAL(0): discordance in the mnemonics. Then, having started along these lines, a rewrite was provoked, prompted by the recollection that function ISPRIME does not engage in the standard slog through possible prime factors (except for two), since for odd numbers it refers to its big bit array. Accessing this array takes time as it is in a disc file, but the operating system buffers popular records in memory (a record is 4096 bytes for 32736 bits as each starts with a four-byte count, thus the first record spans 3 to 65473), so timing runs is a frustrating business. There seemed no gross change in speed, so that's good enough for a demonstration. The code involves a GO TO statement because there is no repeat ... until test construction provided in Fortran and a DO WHILE ... END DO would involve a wasted first test. Because I really hate array bound errors there is a check against LASTP even though the array will never overflow for INTEGER*4, but (potentially) someday the code might be inflated to INTEGER*8 or some other larger capacity and the necessary adjustments be overlooked. One could have IF (LASTP.LE.9 .AND. HUGE(N).GT.2147483648) STOP "Oi! INTEGER*4 usage!" to check this (and a good compiler would convert it to no code if all was well) but that's tiresome too and only checks for some problems. Accordingly, the code for adding a factor to the list is too messy to replicate, and making it into a service subroutine is tiresome: thus does structure falter when spaghetti is not forgotten.

Similarly, initial attempts foundered before I realised that the sum of the digits of the prime factors did not mean that of the unique prime factors once only but included each appearance of a prime factor, so it was DIGITSUM(F.PVAL(i),BASE)*F.PPOW(i) for success. And, since one is deemed to have no prime factors, one does not appear even though it is not skipped as being a prime number.

The factorisation is represented in a data aggregate, which is returned by function FACTOR. This is a facility introduced with F90, and before that one would have to use a collection of ordinary arrays to identify the list of primes and powers of a factorisation because functions could only return simple variables. Also, earlier compilers did not allow the use of the function's name as a variable within the function, or might allow this but produce incorrect results. However, modern facilities are not always entirely beneficial. Here, the function returns a full set of data for type FACTORED, even though often only the first few elements of the arrays will be needed and the rest could be ignored. It is possible to declare the arrays of type FACTORED to be "allocatable" with their size being determined at run time for each invocation of function FACTOR, at the cost of a lot of additional syntax and statements, plus the common annoyance of not knowing "how big" until after the list has been produced. Alas, such arrangements incur a performance penalty with every reference to the allocatable entities. See for example Sequence_of_primorial_primes#Run-time_allocation

For layout purposes, the numbers found were stashed in a line buffer rather than attempt to mess with the latter-day facilities of "non-advancing" output. This should be paramaterised for documentation purposes with say MBUF = 20 rather than just using the magic constant of 20, however getting that into the FORMAT statement would require FORMAT(<MBUF>I6) and this <n> facility may not be recognised. Alternatively, one could put FORMAT(666I6) and hope that MBUF would never exceed 666.
      MODULE FACTORISE	!Produce a little list...
USE PRIMEBAG !This is a common need.
INTEGER LASTP !Some size allowances.
PARAMETER (LASTP = 9) !2*3*5*7*11*13*17*19*23*29 = 6,469,693,230, > 2,147,483,647.
TYPE FACTORED !Represent a number fully factored.
INTEGER PVAL(0:LASTP) !As a list of prime number indices with PVAL(0) the count.
INTEGER PPOW(LASTP) !And the powers. for the fingered primes.
END TYPE FACTORED !Rather than as a simple number multiplied out.
 
CONTAINS !Now for the details.
SUBROUTINE SHOWFACTORS(N) !First, to show an internal data structure.
TYPE(FACTORED) N !It is supplied as a list of prime factors.
INTEGER I !A stepper.
DO I = 1,N.PVAL(0) !Step along the list.
IF (I.GT.1) WRITE (MSG,"('x',$)") !Append a glyph for "multiply".
WRITE (MSG,"(I0,$)") N.PVAL(I) !The prime number's value.
IF (N.PPOW(I).GT.1) WRITE (MSG,"('^',I0,$)") N.PPOW(I) !With an interesting power?
END DO !On to the next element in the list.
WRITE (MSG,1) N.PVAL(0) !End the line
1 FORMAT (": Factor count ",I0) !With a count of prime factors.
END SUBROUTINE SHOWFACTORS !Hopefully, this will not be needed often.
 
TYPE(FACTORED) FUNCTION FACTOR(IT) !Into a list of primes and their powers.
Careful! 1 is not a factor of N, but if N is prime, N is. N = product of its prime factors.
INTEGER IT,N !The number and a similar style copy to damage.
INTEGER F,FP !A factor and a power.
IF (IT.LE.0) STOP "Factor only positive numbers!" !Or else...
FACTOR.PVAL(0) = 0 !No prime factors have been found. One need not apply.
F = 0 !NEXTPRIME(F) will return 2, the first factor to try.
N = IT !A copy I can damage.
Collapse N into its prime factors.
10 DO WHILE(N.GT.1) !Carthaga delenda est?
IF (ISPRIME(N)) THEN!If the remnant is a prime number,
F = N !Then it is the last factor.
FP = 1 !Its power is one.
N = 1 !And the reduction is finished.
ELSE !Otherwise, continue trying larger factors.
FP = 0 !It has no power yet.
11 F = NEXTPRIME(F) !Go for the next possible factor.
DO WHILE(MOD(N,F).EQ.0) !Well?
FP = FP + 1 !Count a factor..
N = N/F !Reduce the number.
END DO !Until F's multiplicity is exhausted.
IF (FP.LE.0) GO TO 11 !No presence? Try the next factor: N has some...
END IF !One way or another, F is a prime factor and FP its power.
IF (FACTOR.PVAL(0).GE.LASTP) THEN !Have I room in the list?
WRITE (MSG,1) IT,LASTP !Alas.
1 FORMAT ("Factoring ",I0," but with provision for only ", !This shouldn't happen,
1 I0," distinct prime factors!") !If LASTP is correct for the current INTEGER size.
CALL SHOWFACTORS(FACTOR) !Show what has been found so far.
STOP "Not enough storage!" !Quite.
END IF !But normally,
FACTOR.PVAL(0) = FACTOR.PVAL(0) + 1 !Admit another factor.
FACTOR.PVAL(FACTOR.PVAL(0)) = F !The prime number found to be a factor.
FACTOR.PPOW(FACTOR.PVAL(0)) = FP !Place its power.
END DO !Now seee what has survived.
END FUNCTION FACTOR !Thus, a list of primes and their powers.
END MODULE FACTORISE !Careful! PVAL(0) is the number of prime factors.
 
MODULE SMITHSTUFF !Now for the strange stuff.
CONTAINS !The two special workers.
INTEGER FUNCTION DIGITSUM(N,BASE) !Sums the digits of N.
INTEGER N,IT !The number, and a copy I can damage.
INTEGER BASE !The base for arithmetic,
IF (N.LT.0) STOP "DigitSum: negative numbers need not apply!"
DIGITSUM = 0 !Here we go.
IT = N !This value will be damaged.
DO WHILE(IT.GT.0) !Something remains?
DIGITSUM = MOD(IT,BASE) + DIGITSUM !Yes. Grap the low-order digit.
IT = IT/BASE !And descend a power.
END DO !Perhaps something still remains.
END FUNCTION DIGITSUM !Numerology.
 
LOGICAL FUNCTION SMITHNUM(N,BASE) !Worse numerology.
USE FACTORISE !To find the prime factord of N.
INTEGER N !The number of interest.
INTEGER BASE !The base of the numerology.
TYPE(FACTORED) F !A list.
INTEGER I,FD !Assistants.
F = FACTOR(N) !Hopefully, LASTP is large enough for N.
c write (6,"(a,I0,1x)",advance="no") "N=",N
c call ShowFactors(F)
FD = 0 !Attempts via the SUM facility involved too many requirements.
DO I = 1,F.PVAL(0) !For each of the prime factors found...
FD = DIGITSUM(F.PVAL(I),BASE)*F.PPOW(I) + FD !Not forgetting the multiplicity.
END DO !On to the next prime factor in the list.
SMITHNUM = FD.EQ.DIGITSUM(N,BASE) !This is the rule.
END FUNCTION SMITHNUM !So, is N a joker?
END MODULE SMITHSTUFF !Simple enough.
 
USE PRIMEBAG !Gain access to GRASPPRIMEBAG.
USE SMITHSTUFF !The special stuff.
INTEGER LAST !Might as well document this.
PARAMETER (LAST = 9999) !The specification is BELOW 10000...
INTEGER I,N,BASE !Workers.
INTEGER NB,BAG(20) !Prepare a line's worth of results.
MSG = 6 !Standard output.
 
WRITE (MSG,1) LAST !Hello.
1 FORMAT ('To find the "Smith" numbers up to ',I0)
IF (.NOT.GRASPPRIMEBAG(66)) STOP "Gan't grab my file!" !Attempt in hope.
 
10 DO BASE = 2,12 !Flexible numerology.
WRITE (MSG,11) BASE !Here we go again.
11 FORMAT (/,"Working in base ",I0)
N = 0 !None found.
NB = 0 !So, none are bagged.
DO I = 1,LAST !Step through the span.
IF (ISPRIME(I)) CYCLE !Prime numbers are boring Smith numbers. Skip them.
IF (SMITHNUM(I,BASE)) THEN !So?
N = N + 1 !Count one in.
IF (NB.GE.20) THEN !A full line's worth with another to come?
WRITE (MSG,12) BAG !Yep. Roll the line to make space.
12 FORMAT (20I6) !This will do for a nice table.
NB = 0 !The line is now ready.
END IF !So much for a line buffer.
NB = NB + 1 !Count another entry.
BAG(NB) = I !Place it.
END IF !So much for a Smith style number.
END DO !On to the next candidate number.
WRITE (MSG,12) BAG(1:NB)!Wave the tail end.
WRITE (MSG,13) N !Save the human some counting.
13 FORMAT (I9," found.") !Just in case.
END DO !On to the next base.
END !That was strange.

Output: selecting the base ten result:

Working in base 10
     4    22    27    58    85    94   121   166   202   265   274   319   346   355   378   382   391   438   454   483
   517   526   535   562   576   588   627   634   636   645   648   654   663   666   690   706   728   729   762   778
...etc
  9346  9355  9382  9386  9387  9396  9414  9427  9483  9522  9535  9571  9598  9633  9634  9639  9648  9657  9684  9708
  9717  9735  9742  9760  9778  9840  9843  9849  9861  9880  9895  9924  9942  9968  9975  9985
      376 found.

For the various bases, the counts were

Base:     2   3   4   5   6   7   8   9  10  11  12
Count:  615 459 417 327 716 245 432 250 376 742 448

Reverting to counting each prime of a factorisation once only did not simply reject all those Smith numbers that had repeated prime factors, it added new entries, for example 9940: the "smith" numbers?

Working in base 10
    22    58    84    85    94   136   160   166   202   234   250   265   274   308   319   336   346   355   361   364
   382   391   424   438   454   456   476   483   516   517   526   535   562   627   634   644   645   650   654   660
   663   690   702   706   732   735   762   778   855   860   861   895   913   915   922   948   958   985  1086  1111
  1116  1148  1165  1219  1255  1282  1312  1344  1404  1484  1507  1550  1576  1581  1600  1612  1626  1633  1642  1650
  1665  1678  1708  1752  1795  1812  1822  1824  1842  1858  1876  1894  1903  1921  1924  1966  2008  2038  2064  2067
  2106  2155  2166  2173  2182  2218  2227  2232  2236  2265  2275  2325  2326  2352  2356  2362  2373  2401  2409  2434
  2461  2500  2515  2541  2565  2578  2605  2614  2616  2625  2640  2679  2722  2751  2760  2785  2826  2839  2872  2902
  2911  2924  2958  2960  2965  2974  3036  3042  3046  3048  3091  3138  3164  3172  3226  3246  3268  3285  3339  3344
  3345  3381  3390  3393  3442  3474  3476  3484  3505  3552  3556  3592  3595  3615  3618  3622  3625  3630  3649  3694
  3712  3736  3792  3802  3836  3850  3865  3892  3912  3920  3930  3933  3946  3973  4024  4054  4116  4126  4148  4160
  4162  4173  4188  4189  4191  4198  4209  4212  4228  4235  4268  4275  4279  4306  4344  4369  4396  4414  4456  4460
  4473  4564  4590  4594  4636  4656  4676  4702  4744  4765  4770  4776  4794  4820  4824  4844  4855  4905  4918  4920
  4954  4974  4980  4981  5022  5052  5062  5068  5071  5094  5098  5145  5150  5168  5176  5242  5253  5268  5269  5298
  5305  5332  5344  5348  5386  5397  5412  5422  5425  5458  5464  5484  5485  5525  5539  5548  5602  5612  5638  5642
  5652  5674  5715  5742  5752  5818  5840  5854  5874  5926  5935  5946  5998  6016  6027  6054  6060  6066  6115  6175
  6178  6184  6187  6244  6259  6260  6295  6315  6356  6364  6385  6390  6439  6457  6472  6475  6500  6502  6504  6512
  6524  6531  6564  6567  6583  6585  6596  6600  6603  6604  6616  6620  6633  6692  6693  6702  6714  6718  6741  6835
  6855  6900  6904  6934  6950  6960  6980  6981  7008  7026  7028  7038  7048  7051  7052  7062  7076  7078  7089  7150
  7186  7195  7196  7212  7228  7236  7249  7268  7287  7335  7339  7362  7364  7402  7428  7438  7447  7465  7503  7506
  7525  7624  7627  7650  7674  7683  7726  7756  7762  7782  7809  7834  7850  7915  7924  7978  8005  8014  8023  8076
  8077  8084  8091  8095  8145  8149  8158  8164  8185  8214  8224  8244  8257  8277  8284  8292  8308  8325  8334  8347
  8415  8420  8421  8466  8508  8518  8545  8600  8653  8673  8720  8724  8754  8780  8790  8816  8851  8914  8924  8932
  8955  8982  9015  9028  9031  9052  9094  9096  9116  9166  9180  9193  9229  9274  9285  9294  9301  9306  9330  9333
  9346  9350  9355  9382  9412  9425  9427  9436  9483  9528  9535  9540  9571  9598  9630  9634  9650  9652  9711  9716
  9717  9735  9742  9772  9778  9843  9861  9895  9916  9940  9942  9985
      492 found.

FreeBASIC[edit]

' FB 1.05.0 Win64
 
Sub getPrimeFactors(factors() As UInteger, n As UInteger)
If n < 2 Then Return
Dim factor As UInteger = 2
Do
If n Mod factor = 0 Then
Redim Preserve factors(0 To UBound(factors) + 1)
factors(UBound(factors)) = factor
n \= factor
If n = 1 Then Return
Else
' non-prime factors will always give a remainder > 0 as their own factors have already been removed
' so it's not worth checking that the next potential factor is prime
factor += 1
End If
Loop
End Sub
 
Function sumDigits(n As UInteger) As UInteger
If n < 10 Then Return n
Dim sum As UInteger = 0
While n > 0
sum += n Mod 10
n \= 10
Wend
Return sum
End Function
 
Function isSmith(n As UInteger) As Boolean
If n < 2 Then Return False
Dim factors() As UInteger
getPrimeFactors factors(), n
If UBound(factors) = 0 Then Return False '' n must be prime if there's only one factor
Dim primeSum As UInteger = 0
For i As UInteger = 0 To UBound(factors)
primeSum += sumDigits(factors(i))
Next
Return sumDigits(n) = primeSum
End Function
 
Print "The Smith numbers below 10000 are : "
Print
Dim count As UInteger = 0
For i As UInteger = 2 To 9999
If isSmith(i) Then
Print Using "#####"; i;
count += 1
End If
Next
Print : Print
Print count; " numbers found"
Print
Print "Press any key to quit"
Sleep
Output:
The Smith numbers below 10000 are :

    4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382
  391  438  454  483  517  526  535  562  576  588  627  634  636  645  648  654
  663  666  690  706  728  729  762  778  825  852  861  895  913  915  922  958
  985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678
 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962
 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409
 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751
 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168
 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663
 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191
 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788
 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242
 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642
 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115
 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583
 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062
 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503
 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978
 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347
 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851
 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285
 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571
 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849
 9861 9880 9895 9924 9942 9968 9975 9985

376 numbers found

Go[edit]

Translation of: C
 
package main
 
import "fmt"
 
func numPrimeFactors(x uint) int {
var p uint = 2
var pf int
if x == 1 {
return 1
}
for {
if (x % p) == 0 {
pf++
x /= p
if x == 1 {
return pf
}
} else {
p++
}
}
}
 
func primeFactors(x uint, arr []uint) {
var p uint = 2
var pf int
if x == 1 {
arr[pf] = 1
return
}
for {
if (x % p) == 0 {
arr[pf] = p
pf++
x /= p
if x == 1 {
return
}
} else {
p++
}
}
}
 
func sumDigits(x uint) uint {
var sum uint
for x != 0 {
sum += x % 10
x /= 10
}
return sum
}
 
func sumFactors(arr []uint, size int) uint {
var sum uint
for a := 0; a < size; a++ {
sum += sumDigits(arr[a])
}
return sum
}
 
func listAllSmithNumbers(maxSmith uint) {
var arr []uint
var a uint
for a = 4; a < maxSmith; a++ {
numfactors := numPrimeFactors(a)
arr = make([]uint, numfactors)
if numfactors < 2 {
continue
}
primeFactors(a, arr)
if sumDigits(a) == sumFactors(arr, numfactors) {
fmt.Printf("%4d ", a)
}
}
}
 
func main() {
const maxSmith = 10000
fmt.Printf("All the Smith Numbers less than %d are:\n", maxSmith)
listAllSmithNumbers(maxSmith)
fmt.Println()
}
 
Output:

All the Smith Numbers less than 10000 are:

  4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382  391  438  454  483  517  526  535  562  576  588  627  634  636  645  648  654  663  666  690  706  728  729  762  778  825  852  861  895  913  915  922  958  985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 56425674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985

Haskell[edit]

import Data.Tuple (swap)
import Data.List (unfoldr)
 
isSmith :: Int -> Bool
isSmith n = pfs /= [n] && sumDigits n == foldr ((+) . sumDigits) 0 pfs
where
sumDigits = sum . baseDigits 10
root = floor . sqrt . fromIntegral
pfs = primeFactors n
primeFactors n =
let fs = take 1 $ filter ((0 ==) . rem n) [2 .. root n]
in case fs of
[] -> [n]
_ -> fs ++ primeFactors (div n (head fs))
 
baseDigits :: Int -> Int -> [Int]
baseDigits base = unfoldr remQuot
where
remQuot 0 = Nothing
remQuot x = Just (swap (quotRem x base))
 
lowSmiths :: [Int]
lowSmiths = filter isSmith [2 .. 9999]
 
lowSmithCount :: Int
lowSmithCount = length lowSmiths
 
main :: IO ()
main =
mapM_
putStrLn
[ "Count of Smith Numbers below 10k:"
, show lowSmithCount
, "\nFirst 15 Smith Numbers:"
, unwords (show <$> take 15 lowSmiths)
, "\nLast 12 Smith Numbers below 10k:"
, unwords (show <$> drop (lowSmithCount - 12) lowSmiths)
]
Output:
Count of Smith Numbers below 10k:
376

First 15 Smith Numbers:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378

Last 12 Smith Numbers below 10k:
9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985

J[edit]

Implementation:

digits=: 10&#.inv
sumdig=: +/@,@digits
notprime=: [email protected](1&p:)
smith=: #~ notprime * (=&sumdig q:)every

Task example:

   #smith }.i.10000
376
q:376
2 2 2 47
47 8$smith }.i.10000
4 22 27 58 85 94 121 166
202 265 274 319 346 355 378 382
391 438 454 483 517 526 535 562
576 588 627 634 636 645 648 654
663 666 690 706 728 729 762 778
825 852 861 895 913 915 922 958
985 1086 1111 1165 1219 1255 1282 1284
1376 1449 1507 1581 1626 1633 1642 1678
1736 1755 1776 1795 1822 1842 1858 1872
1881 1894 1903 1908 1921 1935 1952 1962
1966 2038 2067 2079 2155 2173 2182 2218
2227 2265 2286 2326 2362 2366 2373 2409
2434 2461 2475 2484 2515 2556 2576 2578
2583 2605 2614 2679 2688 2722 2745 2751
2785 2839 2888 2902 2911 2934 2944 2958
2964 2965 2970 2974 3046 3091 3138 3168
3174 3226 3246 3258 3294 3345 3366 3390
3442 3505 3564 3595 3615 3622 3649 3663
3690 3694 3802 3852 3864 3865 3930 3946
3973 4054 4126 4162 4173 4185 4189 4191
4198 4209 4279 4306 4369 4414 4428 4464
4472 4557 4592 4594 4702 4743 4765 4788
4794 4832 4855 4880 4918 4954 4959 4960
4974 4981 5062 5071 5088 5098 5172 5242
5248 5253 5269 5298 5305 5386 5388 5397
5422 5458 5485 5526 5539 5602 5638 5642
5674 5772 5818 5854 5874 5915 5926 5935
5936 5946 5998 6036 6054 6084 6096 6115
6171 6178 6187 6188 6252 6259 6295 6315
6344 6385 6439 6457 6502 6531 6567 6583
6585 6603 6684 6693 6702 6718 6760 6816
6835 6855 6880 6934 6981 7026 7051 7062
7068 7078 7089 7119 7136 7186 7195 7227
7249 7287 7339 7402 7438 7447 7465 7503
7627 7674 7683 7695 7712 7726 7762 7764
7782 7784 7809 7824 7834 7915 7952 7978
8005 8014 8023 8073 8077 8095 8149 8154
8158 8185 8196 8253 8257 8277 8307 8347
8372 8412 8421 8466 8518 8545 8568 8628
8653 8680 8736 8754 8766 8790 8792 8851
8864 8874 8883 8901 8914 9015 9031 9036
9094 9166 9184 9193 9229 9274 9276 9285
9294 9296 9301 9330 9346 9355 9382 9386
9387 9396 9414 9427 9483 9522 9535 9571
9598 9633 9634 9639 9648 9657 9684 9708
9717 9735 9742 9760 9778 9840 9843 9849
9861 9880 9895 9924 9942 9968 9975 9985

(first we count how many smith numbers are in our result, then we look at the prime factors of that count - turns out that 8 columns of 47 numbers each is perfect for this task.)

Java[edit]

Works with: Java version 7
import java.util.*;
 
public class SmithNumbers {
 
public static void main(String[] args) {
for (int n = 1; n < 10_000; n++) {
List<Integer> factors = primeFactors(n);
if (factors.size() > 1) {
int sum = sumDigits(n);
for (int f : factors)
sum -= sumDigits(f);
if (sum == 0)
System.out.println(n);
}
}
}
 
static List<Integer> primeFactors(int n) {
List<Integer> result = new ArrayList<>();
 
for (int i = 2; n % i == 0; n /= i)
result.add(i);
 
for (int i = 3; i * i <= n; i += 2) {
while (n % i == 0) {
result.add(i);
n /= i;
}
}
 
if (n != 1)
result.add(n);
 
return result;
}
 
static int sumDigits(int n) {
int sum = 0;
while (n > 0) {
sum += (n % 10);
n /= 10;
}
return sum;
}
}
4
22
27
58
85
94
121
...
9924
9942
9968
9975
9985

JavaScript[edit]

ES6[edit]

Translation of: Haskell
(() => {
'use strict';
 
// GENERIC FUNCTIONS -----------------------------------------------------
 
// concat :: [[a]] -> [a] | [String] -> String
const concat = xs => {
if (xs.length > 0) {
const unit = typeof xs[0] === 'string' ? '' : [];
return unit.concat.apply(unit, xs);
} else return [];
}
 
// range :: Int -> Int -> [Int]
const range = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);
 
// dropWhile :: (a -> Bool) -> [a] -> [a]
const dropWhile = (p, xs) => {
let i = 0;
for (let lng = xs.length;
(i < lng) && p(xs[i]); i++) {}
return xs.slice(i);
}
 
// head :: [a] -> a
const head = xs => xs.length ? xs[0] : undefined;
 
// Int -> [a] -> [a]
const take = (n, xs) => xs.slice(0, n);
 
// drop :: Int -> [a] -> [a]
const drop = (n, xs) => xs.slice(n);
 
// floor :: Num a => a -> Int
const floor = Math.floor;
 
// floor :: Num -> Num
const sqrt = Math.sqrt;
 
// show :: a -> String
const show = x => JSON.stringify(x, null, 2);
 
// unwords :: [String] -> String
const unwords = xs => xs.join(' ');
 
 
// MAIN -----------------------------------------------------------------
 
// primeFactors :: Int -> [Int]
const primeFactors = n => {
const fs = take(1, (dropWhile(x => n % x !== 0, range(2, floor(sqrt(n))))));
return fs.length === 0 ? (
[n]
) : fs.concat(primeFactors(floor(n / head(fs))));
};
 
// digitSum :: [Char] -> Int
const digitSum = ds =>
ds
.reduce((a, b) => parseInt(a, 10) + parseInt(b, 10), 0);
 
// isSmith :: Int -> Bool
const isSmith = n => {
const pfs = primeFactors(n);
return (head(pfs) !== n) &&
digitSum(n.toString()
.split('')) == digitSum(
concat(pfs.map(x => x.toString()))
.split('')
);
}
 
// TEST ------------------------------------------------------------------
 
// lowSmiths :: [Int]
const lowSmiths = range(2, 9999)
.filter(isSmith);
 
// lowSmithCount :: Int
const lowSmithCount = lowSmiths.length;
 
return [
"Count of Smith Numbers below 10k:",
show(lowSmithCount),
"\nFirst 15 Smith Numbers:",
unwords(take(15, lowSmiths)),
"\nLast 12 Smith Numbers below 10000:",
unwords(drop(lowSmithCount - 12, lowSmiths))
].join('\n');
})();
Output:
Count of Smith Numbers below 10k:
376

First 15 Smith Numbers:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378

Last 12 Smith Numbers below 10000:
9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985

Julia[edit]

# v0.6
 
function sumdigits(n::Integer)
sum = 0
while n > 0
sum += n % 10
n = div(n, 10)
end
return sum
end
 
using Primes
issmith(n::Integer) = !isprime(n) && sumdigits(n) == sum(sumdigits(f) for f in factor(Vector, n))
 
smithnumbers = collect(n for n in 2:10000 if issmith(n))
println("Smith numbers up to 10000:\n$smithnumbers")
Output:
Smith numbers up to 10000:
[4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535,
562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913,
915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678,
1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038,
2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484,
2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934,
2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390,
3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054,
4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594,
4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098,
5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642,
5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178,
6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693,
6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186,
7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764,
7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185,
8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754,
8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274,
9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571,
9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880,
9895, 9924, 9942, 9968, 9975, 9985]

Kotlin[edit]

Translation of: FreeBASIC
// version 1.0.6
 
fun getPrimeFactors(n: Int): MutableList<Int> {
val factors = mutableListOf<Int>()
if (n < 2) return factors
var factor = 2
var nn = n
while (true) {
if (nn % factor == 0) {
factors.add(factor)
nn /= factor
if (nn == 1) return factors
}
else if (factor >= 3) factor += 2
else factor = 3
}
}
 
fun sumDigits(n: Int): Int = when {
n < 10 -> n
else -> {
var sum = 0
var nn = n
while (nn > 0) {
sum += (nn % 10)
nn /= 10
}
sum
}
}
 
fun isSmith(n: Int): Boolean {
if (n < 2) return false
val factors = getPrimeFactors(n)
if (factors.size == 1) return false
val primeSum = factors.sumBy { sumDigits(it) }
return sumDigits(n) == primeSum
}
 
fun main(args: Array<String>) {
println("The Smith numbers below 10000 are:\n")
var count = 0
for (i in 2 until 10000) {
if (isSmith(i)) {
print("%5d".format(i))
count++
}
}
println("\n\n$count numbers found")
}
Output:
    4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382
  391  438  454  483  517  526  535  562  576  588  627  634  636  645  648  654
  663  666  690  706  728  729  762  778  825  852  861  895  913  915  922  958
  985 1086 1111 1165 1219 1255 1282 1284 1376 1449 1507 1581 1626 1633 1642 1678
 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962
 1966 2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409
 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679 2688 2722 2745 2751
 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168
 3174 3226 3246 3258 3294 3345 3366 3390 3442 3505 3564 3595 3615 3622 3649 3663
 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191
 4198 4209 4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788
 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088 5098 5172 5242
 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642
 5674 5772 5818 5854 5874 5915 5926 5935 5936 5946 5998 6036 6054 6084 6096 6115
 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583
 6585 6603 6684 6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062
 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447 7465 7503
 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978
 8005 8014 8023 8073 8077 8095 8149 8154 8158 8185 8196 8253 8257 8277 8307 8347
 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851
 8864 8874 8883 8901 8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285
 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535 9571
 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849
 9861 9880 9895 9924 9942 9968 9975 9985

376 numbers found

Lua[edit]

Slightly long-winded prime factor function but it's a bit faster than the 'easy' way.

-- Returns a boolean indicating whether n is prime
function isPrime (n)
if n < 2 then return false end
if n < 4 then return true end
if n % 2 == 0 then return false end
for d = 3, math.sqrt(n), 2 do
if n % d == 0 then return false end
end
return true
end
 
-- Returns a table of the prime factors of n
function primeFactors (n)
local pfacs, divisor = {}, 1
if n < 1 then return pfacs end
while not isPrime(n) do
while not isPrime(divisor) do divisor = divisor + 1 end
while n % divisor == 0 do
n = n / divisor
table.insert(pfacs, divisor)
end
divisor = divisor + 1
if n == 1 then return pfacs end
end
table.insert(pfacs, n)
return pfacs
end
 
-- Returns the sum of the digits of n
function sumDigits (n)
local sum, nStr = 0, tostring(n)
for digit = 1, nStr:len() do
sum = sum + tonumber(nStr:sub(digit, digit))
end
return sum
end
 
-- Returns a boolean indicating whether n is a Smith number
function isSmith (n)
if isPrime(n) then return false end
local sumFacs = 0
for _, v in ipairs(primeFactors(n)) do
sumFacs = sumFacs + sumDigits(v)
end
return sumFacs == sumDigits(n)
end
 
-- Main procedure
for n = 1, 10000 do
if isSmith(n) then io.write(n .. "\t") end
end

Seems silly to paste in all 376 numbers but rest assured the output agrees with https://oeis.org/A006753

Objeck[edit]

use Collection;
 
class Test {
function : Main(args : String[]) ~ Nil {
for(n := 1; n < 10000; n+=1;) {
factors := PrimeFactors(n);
if(factors->Size() > 1) {
sum := SumDigits(n);
each(i : factors) {
sum -= SumDigits(factors->Get(i));
};
 
if(sum = 0) {
n->PrintLine();
};
};
};
}
 
function : PrimeFactors(n : Int) ~ IntVector {
result := IntVector->New();
 
for(i := 2; n % i = 0; n /= i;) {
result->AddBack(i);
};
 
for(i := 3; i * i <= n; i += 2;) {
while(n % i = 0) {
result->AddBack(i);
n /= i;
};
};
 
if(n <> 1) {
result->AddBack(n);
};
 
return result;
}
 
function : SumDigits(n : Int) ~ Int {
sum := 0;
while(n > 0) {
sum += (n % 10);
n /= 10;
};
 
return sum;
}
}
4
22
27
58
85
94
121
166
202
...
9975
9985

Pascal[edit]

Works with: Free Pascal

Using a segmented sieve of erathostenes and mark every number with the index of its prime factor <= sqrt(number). I use a presieved segment to reduce the time for small primes. I thought, it would be a small speed improvement ;-)

the function IncDgtSum delivers the next sum of digits very fast (2.6 s for 1 to 1e9 )

program SmithNum;
{$IFDEF FPC}
{$MODE objFPC} //result and useful for x64
{$CODEALIGN PROC=64}
{$ENDIF}
uses
sysutils;
type
tdigit = byte;
tSum = LongInt;
const
base = 10;
//maxDigitCnt *(base-1) <= High(tSum)
//maxDigitCnt <= High(tSum) DIV (base-1);
maxDigitCnt = 16;
 
StartPrimNo = 6;
csegsieveSIze = 2*3*5*7*11*13;//prime 0..5
type
tDgtSum = record
dgtNum : LongInt;
dgtSum : tSum;
dgts : array[0..maxDigitCnt-1] of tdigit;
end;
tNumFactype = word;
tnumFactor = record
numfacCnt: tNumFactype;
numfacts : array[1..15] of tNumFactype;
end;
tpnumFactor= ^tnumFactor;
 
tsieveprim = record
spPrim : Word;
spDgtsum : Word;
spOffset : LongWord;
end;
tpsieveprim = ^tsieveprim;
 
tsievePrimarr = array[0..6542-1] of tsieveprim;
tsegmSieve = array[1..csegsieveSIze] of tnumFactor;
 
var
Primarr:tsievePrimarr;
copySieve,
actSieve : tsegmSieve;
PrimDgtSum :tDgtSum;
PrimCnt : NativeInt;
 
function IncDgtSum(var ds:tDgtSum):boolean;
//add 1 to dgts and corrects sum of Digits
//return if overflow happens
var
i : NativeInt;
Begin
i := High(ds.dgts);
inc(ds.dgtNum);
repeat
IF ds.dgts[i] < Base-1 then
//add one and done
Begin
inc(ds.dgts[i]);
inc(ds.dgtSum);
BREAK;
end
else
Begin
ds.dgts[i] := 0;
dec(ds.dgtSum,Base-1);
end;
dec(i);
until i < Low(ds.dgts);
result := i < Low(ds.dgts)
end;
 
procedure OutDgtSum(const ds:tDgtSum);
var
i : NativeInt;
Begin
i := Low(ds.dgts);
repeat
write(ds.dgts[i]:3);
inc(i);
until i > High(ds.dgts);
writeln(' sum of digits : ',ds.dgtSum:3);
end;
 
procedure OutSieve(var s:tsegmSieve);
var
i,j : NativeInt;
Begin
For i := Low(s) to High(s) do
with s[i] do
Begin
write(i:6,numfacCnt:4);
For j := 1 to numfacCnt do
write(numFacts[j]:5);
writeln;
end;
end;
 
procedure SieveForPrimes;
// sieve for all primes < High(Word)
var
sieve : array of byte;
pS : pByte;
p,i : NativeInt;
Begin
setlength(sieve,High(Word));
Fillchar(sieve[Low(sieve)],length(sieve),#0);
pS:= @sieve[0]; //zero based
dec(pS);// make it one based
//sieve
p := 2;
repeat
i := p*p;
IF i> High(Word) then
BREAK;
repeat pS[i] := 1; inc(i,p); until i > High(Word);
repeat inc(p) until pS[p] = 0;
until false;
//now fill array of primes
fillchar(PrimDgtSum,SizeOf(PrimDgtSum),#0);
IncDgtSum(PrimDgtSum);//1
i := 0;
For p := 2 to High(Word) do
Begin
IncDgtSum(PrimDgtSum);
if pS[p] = 0 then
Begin
with PrimArr[i] do
Begin
spOffset := 2*p;//start at 2*prime
spPrim := p;
spDgtsum := PrimDgtSum.dgtSum;
end;
inc(i);
end;
end;
PrimCnt := i-1;
end;
 
procedure MarkWithPrime(SpIdx:NativeInt;var sf:tsegmSieve);
var
i : NativeInt;
pSf :^tnumFactor;
MarkPrime : NativeInt;
Begin
with Primarr[SpIdx] do
Begin
MarkPrime := spPrim;
i := spOffSet;
IF i <= csegsieveSize then
Begin
pSf := @sf[i];
repeat
pSf^.numFacts[pSf^.numfacCnt+1] := SpIdx;
inc(pSf^.numfacCnt);
inc(pSf,MarkPrime);
inc(i,MarkPrime);
until i > csegsieveSize;
end;
spOffset := i-csegsieveSize;
end;
end;
 
procedure InitcopySieve(var cs:tsegmSieve);
var
pr: NativeInt;
Begin
fillchar(cs[Low(cs)],sizeOf(cs),#0);
For Pr := 0 to 5 do
Begin
with Primarr[pr] do
spOffset := spPrim;//mark the prime too
MarkWithPrime(pr,cs);
end;
end;
 
procedure MarkNextSieve(var s:tsegmSieve);
var
idx: NativeInt;
Begin
s:= copySieve;
For idx := StartPrimNo to PrimCnt do
MarkWithPrime(idx,s);
end;
 
function DgtSumInt(n: NativeUInt):NativeUInt;
var
r : NativeUInt;
Begin
result := 0;
repeat
r := n div base;
inc(result,n-base*r);
n := r
until r = 0;
end;
 
{function DgtSumOfFac(pN: tpnumFactor;dgtNo:tDgtSum):boolean;}
function TestSmithNum(pN: tpnumFactor;dgtNo:tDgtSum):boolean;
var
i,k,r,dgtSumI,dgtSumTarget : NativeUInt;
pSp:tpsieveprim;
pNumFact : ^tNumFactype;
Begin
i := dgtNo.dgtNum;
dgtSumTarget :=dgtNo.dgtSum;
 
dgtSumI := 0;
with pN^ do
Begin
k := numfacCnt;
pNumFact := @numfacts[k];
end;
 
For k := k-1 downto 0 do
Begin
pSp := @PrimArr[pNumFact^];
r := i DIV pSp^.spPrim;
repeat
i := r;
r := r DIV pSp^.spPrim;
inc(dgtSumI,pSp^.spDgtsum);
until (i - r* pSp^.spPrim) <> 0;
IF dgtSumI > dgtSumTarget then
Begin
result := false;
EXIT;
end;
dec(pNumFact);
end;
If i <> 1 then
inc(dgtSumI,DgtSumInt(i));
result := dgtSumI = dgtSumTarget
end;
 
function CheckSmithNo(var s:tsegmSieve;var dgtNo:tDgtSum;Lmt:NativeInt=csegsieveSIze):NativeUInt;
var
pNumFac : tpNumFactor;
i : NativeInt;
Begin
result := 0;
i := low(s);
pNumFac := @s[i];
For i := i to lmt do
Begin
incDgtSum(dgtNo);
IF pNumFac^.numfacCnt<> 0 then
IF TestSmithNum(pNumFac,dgtNo) then
Begin
inc(result);
//Mark as smith number
inc(pNumFac^.numfacCnt,1 shl 15);
end;
inc(pNumFac);
end;
end;
 
const
limit = 100*1000*1000;
var
actualNo :tDgtSum;
i,s : NativeInt;
Begin
SieveForPrimes;
InitcopySieve(copySieve);
i := 1;
s:= -6;//- 2,3,5,7,11,13
 
fillchar(actualNo,SizeOf(actualNo),#0);
while i < Limit-csegsieveSize do
Begin
MarkNextSieve(actSieve);
inc(s,CheckSmithNo(actSieve,actualNo));
inc(i, csegsieveSize);
end;
//check the rest
MarkNextSieve(actSieve);
inc(s,CheckSmithNo(actSieve,actualNo,Limit-i+1));
write(s:8,' smith-numbers up to ',actualNo.dgtnum:10);
end.
 
Output:
64-Bit FPC 3.1.1 -O3 -Xs  i4330 3.5 Ghz
       6 smith-numbers up to        100
      49 smith-numbers up to       1000
     376 smith-numbers up to      10000
    3294 smith-numbers up to     100000
   29928 smith-numbers up to    1000000 real   0m00.064s
  278411 smith-numbers up to   10000000 real   0m00.661s
 2632758 smith-numbers up to  100000000 real   0m06.981s
25154060 smith-numbers up to 1000000000 real   1m14.077s

  Number of Smith numbers below 10^n.     1
  1:1, 2:6, 3:49, 4:376, 5:3294, 6:29928, 7:278411, 8:2632758,
  9:25154060, 10:241882509, 11:2335807857, 12:22635291815,13:219935518608

Perl[edit]

Library: ntheory
use ntheory qw/:all/;
my @smith;
forcomposites {
push @smith, $_ if sumdigits($_) == sumdigits(join("",factor($_)));
} 10000-1;
say scalar(@smith), " Smith numbers below 10000.";
say "@smith";
Output:
376 Smith numbers below 10000.
4 22 27 58 85 94 121 166 202 ... 9924 9942 9968 9975 9985

Perl 6[edit]

constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime;
 
multi factors ( 1 ) { 1 }
multi factors ( Int $remainder is copy ) {
gather for @primes -> $factor {
 
# if remainder < factor², we're done
if $factor * $factor > $remainder {
take $remainder if $remainder > 1;
last;
}
 
# How many times can we divide by this prime?
while $remainder %% $factor {
take $factor;
last if ($remainder div= $factor) === 1;
}
}
}
# Code above here is verbatim from RC:Count_in_factors#Perl6
 
sub is_smith_number ( Int $n ) {
(!$n.is-prime) and ( [+] $n.comb ) == ( [+] factors($n).join.comb );
}
 
my @s = grep &is_smith_number, 2 ..^ 10_000;
say "{@s.elems} Smith numbers below 10_000";
say 'First 10: ', @s[ ^10 ];
say 'Last 10: ', @s[ *-10 .. * ];
Output:
376 Smith numbers below 10_000
First 10: (4 22 27 58 85 94 121 166 202 265)
Last  10: (9843 9849 9861 9880 9895 9924 9942 9968 9975 9985)

Phix[edit]

Note that the builtin prime_factors(4) yields {2}, rather than {2,2}, hence the inner loop (admittedly repeat..until style would be better, if only Phix had that).

function sum_digits(integer n, integer base=10)
integer res = 0
while n do
res += remainder(n,base)
n = floor(n/base)
end while
return res
end function
 
function smith(integer n)
sequence p = prime_factors(n)
integer sp = 0, w = n
for i=1 to length(p) do
integer pi = p[i],
spi = sum_digits(pi)
while mod(w,pi)=0 do
sp += spi
w = floor(w/pi)
end while
end for
return sum_digits(n)=sp
end function
 
sequence s = {}
for i=1 to 10000 do
if smith(i) then s &= i end if
end for
?length(s)
s[8..-8] = {"..."}
?s
376
{4,22,27,58,85,94,121,"...",9880,9895,9924,9942,9968,9975,9985}

PicoLisp[edit]

(de factor (N)
(make
(let (D 2 L (1 2 2 . (4 2 4 2 4 6 2 6 .)) M (sqrt N))
(while (>= M D)
(if (=0 (% N D))
(setq M (sqrt (setq N (/ N (link D)))))
(inc 'D (pop 'L)) ) )
(link N) ) ) )
(de sumdigits (N)
(sum format (chop N)) )
(de smith (X)
(make
(for N X
(let R (factor N)
(and
(cdr R)
(= (sum sumdigits R) (sumdigits N))
(link N) ) ) ) ) )
(let L (smith 10000)
(println 'first-10 (head 10 L))
(println 'last-10 (tail 10 L))
(println 'all (length L)) )
Output:
first-10 (4 22 27 58 85 94 121 166 202 265)
last-10 (9843 9849 9861 9880 9895 9924 9942 9968 9975 9985)
all 376

PureBasic[edit]

DisableDebugger
#ECHO=#True ; #True: Print all results
Global NewList f.i()
 
Procedure.i ePotenz(Wert.i)
Define.i var=Wert, i
While var
i+1
var/10
Wend
ProcedureReturn i
EndProcedure
 
Procedure.i n_Element(Wert.i,Stelle.i=1)
If Stelle>0
ProcedureReturn (Wert%Int(Pow(10,Stelle))-Wert%Int(Pow(10,Stelle-1)))/Int(Pow(10,Stelle-1))
Else
ProcedureReturn 0
EndIf
EndProcedure
 
Procedure.i qSumma(Wert.i)
Define.i sum, pos
For pos=1 To ePotenz(Wert)
sum+ n_Element(Wert,pos)
Next pos
ProcedureReturn sum
EndProcedure
 
Procedure.b IsPrime(n.i)
Define.i i=5
If n<2 : ProcedureReturn #False : EndIf
If n%2=0 : ProcedureReturn Bool(n=2) : EndIf
If n%3=0 : ProcedureReturn Bool(n=3) : EndIf
While i*i<=n
If n%i=0 : ProcedureReturn #False : EndIf
i+2
If n%i=0 : ProcedureReturn #False : EndIf
i+4
Wend
ProcedureReturn #True
EndProcedure
 
Procedure PFZ(n.i,pf.i=2)
If n>1 And n<>pf
If n%pf=0
AddElement(f()) : f()=pf
PFZ(n/pf,pf)
Else
While Not IsPrime(pf+1) : pf+1 : Wend
PFZ(n,pf+1)
EndIf
ElseIf n=pf
AddElement(f()) : f()=pf
EndIf
EndProcedure
 
OpenConsole("Smith numbers")
;upto=100 : sn=0 : Gosub Smith_loop
;upto=1000 : sn=0 : Gosub Smith_loop
upto=10000 : sn=0 : Gosub Smith_loop
Input()
End
 
Smith_loop:
For i=2 To upto
ClearList(f()) : qs=0
PFZ(i)
CompilerIf #ECHO : Print(Str(i)+~": \t") : CompilerEndIf
ForEach f()
CompilerIf #ECHO : Print(Str(F())+~"\t") : CompilerEndIf
qs+qSumma(f())
Next
If ListSize(f())>1 And qSumma(i)=qs
CompilerIf #ECHO : Print("SMITH-NUMBER") : CompilerEndIf
sn+1
EndIf
CompilerIf #ECHO : PrintN("") : CompilerEndIf
Next
Print(~"\n"+Str(sn)+" Smith number up to "+Str(upto))
Return
Output:
.
.
.
9975:   3       5       5       7       19      SMITH-NUMBER
9976:   2       2       2       29      43
9977:   11      907
9978:   2       3       1663
9979:   17      587
9980:   2       2       5       499
9981:   3       3       1109
9982:   2       7       23      31
9983:   67      149
9984:   2       2       2       2       2       2       2       2       3       13
9985:   5       1997    SMITH-NUMBER
9986:   2       4993
9987:   3       3329
9988:   2       2       11      227
9989:   7       1427
9990:   2       3       3       3       5       37
9991:   97      103
9992:   2       2       2       1249
9993:   3       3331
9994:   2       19      263
9995:   5       1999
9996:   2       2       3       7       7       17
9997:   13      769
9998:   2       4999
9999:   3       3       11      101
10000:  2       2       2       2       5       5       5       5

376 Smith number up To 10000

Python[edit]

 
from sys import stdout
 
 
def factors(n):
rt = []
f = 2
if n == 1:
rt.append(1);
else:
while 1:
if 0 == ( n % f ):
rt.append(f);
n //= f
if n == 1:
return rt
else:
f += 1
return rt
 
 
def sum_digits(n):
sum = 0
while n > 0:
m = n % 10
sum += m
n -= m
n //= 10
 
return sum
 
 
def add_all_digits(lst):
sum = 0
for i in range (len(lst)):
sum += sum_digits(lst[i])
 
return sum
 
 
def list_smith_numbers(cnt):
for i in range(4, cnt):
fac = factors(i)
if len(fac) > 1:
if sum_digits(i) == add_all_digits(fac):
stdout.write("{0} ".format(i) )
 
# entry point
list_smith_numbers(10_000)
 
Output:

4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 ... 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985

Racket[edit]

#lang racket
(require math/number-theory)
 
(define (sum-of-digits n)
(let inr ((n n) (s 0))
(if (zero? n) s (let-values (([q r] (quotient/remainder n 10))) (inr q (+ s r))))))
 
(define (smith-number? n)
(and (not (prime? n))
(= (sum-of-digits n)
(for/sum ((pe (in-list (factorize n))))
(* (cadr pe) (sum-of-digits (car pe)))))))
 
(module+ test
(require rackunit)
(check-equal? (sum-of-digits 0) 0)
(check-equal? (sum-of-digits 33) 6)
(check-equal? (sum-of-digits 30) 3)
 
(check-true (smith-number? 166)))
 
(module+ main
(let loop ((ns (filter smith-number? (range 1 (add1 10000)))))
(unless (null? ns)
(let-values (([l r] (split-at ns (min (length ns) 15))))
(displayln l)
(loop r)))))
Output:
(4 22 27 58 85 94 121 166 202 265 274 319 346 355 378)
(382 391 438 454 483 517 526 535 562 576 588 627 634 636 645)
(648 654 663 666 690 706 728 729 762 778 825 852 861 895 913)

(9396 9414 9427 9483 9522 9535 9571 9598 9633 9634 9639 9648 9657 9684 9708)
(9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975)
(9985)

REXX[edit]

unoptimized[edit]

/*REXX program  finds  (and maybe displays)  Smith  (or joke)  numbers up to a given  N.*/
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N=10000 /*Not specified? Then use the default.*/
tell= (N>0); N=abs(N) - 1 /*use the │N│ for computing (below).*/
w=length(N) /*W: used for aligning Smith numbers. */
#=0 /*#: Smith numbers found (so far). */
@=; do j=4 to N; /*process almost all numbers up to N. */
if sumD(j) \== sumfactr(j) then iterate /*Not a Smith number? Then ignore it.*/
#=#+1 /*bump the Smith number counter. */
if \tell then iterate /*Not showing the numbers? Keep looking*/
@[email protected] right(j, w); if length(@)>130 then do; say substr(@, 2); @=; end
end /*j*/ /* [↑] if N>0, then display Smith #s.*/
 
if @\=='' then say substr(@, 2) /*if any residual Smith #s, display 'em*/
say /* [↓] display the number of Smith #s.*/
say # ' Smith numbers found ≤ ' N"." /*display number of Smith numbers found*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
sumD: parse arg x 1 s 2; do d=2 for length(x)-1; s=s+substr(x,d,1); end; return s
/*──────────────────────────────────────────────────────────────────────────────────────*/
sumFactr: procedure; parse arg z; $=0; f=0 /*obtain the Z number. */
do while z//2==0; $=$+2; f=f+1; z=z% 2; end /*maybe add factor of 2*/
do while z//3==0; $=$+3; f=f+1; z=z% 3; end /* " " " " 3*/
/* ___*/
do j=5 by 2 while j<=z & j*j<=n /*minimum of Z or √ N */
if j//3==0 then iterate /*skip factors that ÷ 3*/
do while z//j==0; f=f+1; $=$+sumD(j); z=z%j; end /*maybe reduce Z by J */
end /*j*/ /* [↓] Z: what's left*/
if z\==1 then do; f=f+1; $=$+sumD(z); end /*Residual? Then add Z*/
if f<2 then return 0 /*Prime? Not a Smith#*/
return $ /*else return sum digs.*/

output   when using the default input:

   4   22   27   58   85   94  121  166  202  265  274  319  346  355  378  382  391  438  454  483  517  526  535  562  576  588  627
 634  636  645  648  654  663  666  690  706  728  729  762  778  825  852  861  895  913  915  922  958  985 1086 1111 1165 1219 1255
1282 1284 1376 1449 1507 1581 1626 1633 1642 1678 1736 1755 1776 1795 1822 1842 1858 1872 1881 1894 1903 1908 1921 1935 1952 1962 1966
2038 2067 2079 2155 2173 2182 2218 2227 2265 2286 2326 2362 2366 2373 2409 2434 2461 2475 2484 2515 2556 2576 2578 2583 2605 2614 2679
2688 2722 2745 2751 2785 2839 2888 2902 2911 2934 2944 2958 2964 2965 2970 2974 3046 3091 3138 3168 3174 3226 3246 3258 3294 3345 3366
3390 3442 3505 3564 3595 3615 3622 3649 3663 3690 3694 3802 3852 3864 3865 3930 3946 3973 4054 4126 4162 4173 4185 4189 4191 4198 4209
4279 4306 4369 4414 4428 4464 4472 4557 4592 4594 4702 4743 4765 4788 4794 4832 4855 4880 4918 4954 4959 4960 4974 4981 5062 5071 5088
5098 5172 5242 5248 5253 5269 5298 5305 5386 5388 5397 5422 5458 5485 5526 5539 5602 5638 5642 5674 5772 5818 5854 5874 5915 5926 5935
5936 5946 5998 6036 6054 6084 6096 6115 6171 6178 6187 6188 6252 6259 6295 6315 6344 6385 6439 6457 6502 6531 6567 6583 6585 6603 6684
6693 6702 6718 6760 6816 6835 6855 6880 6934 6981 7026 7051 7062 7068 7078 7089 7119 7136 7186 7195 7227 7249 7287 7339 7402 7438 7447
7465 7503 7627 7674 7683 7695 7712 7726 7762 7764 7782 7784 7809 7824 7834 7915 7952 7978 8005 8014 8023 8073 8077 8095 8149 8154 8158
8185 8196 8253 8257 8277 8307 8347 8372 8412 8421 8466 8518 8545 8568 8628 8653 8680 8736 8754 8766 8790 8792 8851 8864 8874 8883 8901
8914 9015 9031 9036 9094 9166 9184 9193 9229 9274 9276 9285 9294 9296 9301 9330 9346 9355 9382 9386 9387 9396 9414 9427 9483 9522 9535
9571 9598 9633 9634 9639 9648 9657 9684 9708 9717 9735 9742 9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985

376  Smith numbers found  ≤  9999.

optimized[edit]

This REXX version uses a faster version of the   sumFactr   function;   it's over   20   times faster than the
unoptimized version using a (negative) one million for   N.

/*REXX program  finds  (and maybe displays)  Smith  (or joke)  numbers up to a given  N.*/
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N=10000 /*Not specified? Then use the default.*/
tell= (N>0); N=abs(N) - 1 /*use the │N│ for computing (below).*/
#=0 /*the number of Smith numbers (so far).*/
w=length(N) /*W: used for aligning Smith numbers. */
@=; do j=4 for max(0, N-3) /*process almost all numbers up to N. */
if sumD(j) \== sumFactr(j) then iterate /*Not a Smith number? Then ignore it.*/
#=#+1 /*bump the Smith number counter. */
if \tell then iterate /*Not showing the numbers? Keep looking*/
@[email protected] right(j, w); if length(@)>130 then do; say substr(@, 2); @=; end
end /*j*/ /* [↑] if N>0, then display Smith #s.*/
 
if @\=='' then say substr(@, 2) /*if any residual Smith #s, display 'em*/
say /* [↓] display the number of Smith #s.*/
say # ' Smith numbers found ≤ ' max(0,N)"." /*display number of Smith numbers found*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
sumD: parse arg x 1 s 2; do d=2 for length(x)-1; s=s+substr(x,d,1); end; return s
/*──────────────────────────────────────────────────────────────────────────────────────*/
sumFactr: procedure; parse arg z; $=0; f=0 /*obtain Z number (arg1).*/
do while z// 2==0; $=$+ 2; f=f+1; z=z% 2; end /*maybe add factor of 2. */
do while z// 3==0; $=$+ 3; f=f+1; z=z% 3; end /* " " " " 3. */
do while z// 5==0; $=$+ 5; f=f+1; z=z% 5; end /* " " " " 5. */
do while z// 7==0; $=$+ 7; f=f+1; z=z% 7; end /* " " " " 7. */
t=z; r=0; q=1; do while q<=t; q=q*4; end /*R: will be the iSqrt(Z).*/
do while q>1; q=q%4; _=t-r-q; r=r%2; if _>=0 then do; t=_; r=r+q; end
end /*while q>1*/ /* [↑] compute int. SQRT(Z)*/
 
do j=11 by 6 to r while j<=z /*skip factors that are ÷ 3*/
parse var j '' -1 _; if _\==5 then, /*is last dec. digit ¬a 5 ?*/
do while z//j==0; f=f+1; $=$+sumD(j); z=z%j; end /*maybe reduce Z by J*/
if _==3 then iterate; y=j+2
do while z//y==0; f=f+1; $=$+sumD(y); z=z%y; end /*maybe reduce Z by Y*/
end /*j*/ /* [↓] Z is what's left. */
if z\==1 then do; f=f+1; $=$+sumD(z); end /*if a residual, then add Z*/
if f<2 then return 0 /*Is prime? It's not Smith#*/
return $ /*else, return sum of digs.*/

output   when using the input of (negative) one million:   -1000000

29928  Smith numbers found  ≤  999999.

Ring[edit]

 
# Project : Smith numbers
# Date  : 2017/10/01
# Author  : Gal Zsolt (~ CalmoSoft ~)
# Email  : <[email protected]>
 
see "All the Smith Numbers < 1000 are:" + nl
 
for prime = 1 to 1000
decmp = []
sum1 = sumDigits(prime)
decomp(prime)
sum2 = 0
if len(decmp)>1
for n=1 to len(decmp)
cstr = string(decmp[n])
for m= 1 to len(cstr)
sum2 = sum2 + number(cstr[m])
next
next
ok
if sum1 = sum2
see "" + prime + " "
ok
next
 
func decomp nr
for i = 1 to nr
if isPrime(i) and nr % i = 0
add(decmp, i)
pr = i
while true
pr = pr * i
if nr%pr = 0
add(decmp, i)
else
exit
ok
end
ok
next
 
func isPrime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1
 
func sumDigits n
sum = 0
while n > 0.5
m = floor(n / 10)
digit = n - m * 10
sum = sum + digit
n = m
end
return sum
 

Output:

All the Smith Numbers < 10000 are:
4 22 27 58 85 94 121 166 202 265 274 319 346 355 378 382 391 438 454 483 517 526 535 562 576 588 627 634 636 645 648 654 663 666 690 706 728 729 762 778 825 852 861 895 913 915 922 958 985 

Ruby[edit]

require "prime"
 
class Integer
 
def smith?
return false if prime?
digits.sum == prime_division.map{|pr,n| pr.digits.sum * n}.sum
end
 
end
 
n = 10_000
res = 1.upto(n).select(&:smith?)
 
puts "#{res.size} smith numbers below #{n}:
#{res.first(5).join("
, ")},... #{res.last(5).join(", ")}"
Output:
376 smith numbers below 10000:
4, 22, 27, 58, 85,... 9924, 9942, 9968, 9975, 9985

Rust[edit]

 
fn main () {
//We just need the primes below 100
let primes = vec![2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97];
let mut solution = Vec::new();
let mut number;
for i in 4..10000 {
//Factorize each number below 10.000
let mut prime_factors = Vec::new();
number = i;
for j in &primes {
while number % j == 0 {
number = number / j;
prime_factors.push(j);
}
if number == 1 { break; }
}
//Number is 1 (not a prime factor) if the factorization is complete or a prime bigger than 100
if number != 1 { prime_factors.push(&number); }
//Avoid the prime numbers
if prime_factors.len() < 2 { continue; }
//Check the smith number definition
if prime_factors.iter().fold(0, |n,x| n + x.to_string().chars().map(|d| d.to_digit(10).unwrap()).fold(0, |n,x| n + x))
== i.to_string().chars().map(|d| d.to_digit(10).unwrap()).fold(0, |n,x| n + x) {
solution.push(i);
}
}
println!("Smith numbers below 10000 ({}) : {:?}",solution.len(), solution);
}
 
Output:
Smith numbers below 10000 (376) : [4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966, 2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475, 2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911, 2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366, 3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973, 4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592, 4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088, 5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638, 5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171, 6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684, 6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136, 7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762, 7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158, 8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736, 8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229, 9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535, 9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]

real	0m0.014s
user	0m0.014s
sys	0m0.000s

Sidef[edit]

Translation of: Perl 6
var primes = Enumerator({ |callback|
static primes = Hash()
var p = 2
loop {
callback(p)
p = (primes{p} := p.next_prime)
}
})
 
func factors(remainder) {
 
remainder == 1 && return([remainder])
 
gather {
primes.each { |factor|
if (factor*factor > remainder) {
take(remainder) if (remainder > 1)
break
}
 
while (factor.divides(remainder)) {
take(factor)
break if ((remainder /= factor) == 1)
}
}
}
}
 
func is_smith_number(n) {
 !n.is_prime && (n.digits.sum == factors(n).join.to_i.digits.sum)
}
 
var s = range(2, 10_000).grep { is_smith_number(_) }
say "#{s.len} Smith numbers below 10_000"
say "First 10: #{s.first(10)}"
say "Last 10: #{s.last(10)}"
Output:
376 Smith numbers below 10_000
First 10: [4, 22, 27, 58, 85, 94, 121, 166, 202, 265]
Last  10: [9843, 9849, 9861, 9880, 9895, 9924, 9942, 9968, 9975, 9985]

Tcl[edit]

proc factors {x} {
# list the prime factors of x in ascending order
set result [list]
while {$x % 2 == 0} {
lappend result 2
set x [expr {$x / 2}]
}
for {set i 3} {$i*$i <= $x} {incr i 2} {
while {$x % $i == 0} {
lappend result $i
set x [expr {$x / $i}]
}
}
if {$x != 1} {lappend result $x}
return $result
}
 
proc digitsum {n} {
 ::tcl::mathop::+ {*}[split $n ""]
}
 
proc smith? {n} {
set fs [factors $n]
if {[llength $fs] == 1} {
return false ;# $n is prime
}
expr {[digitsum $n] == [digitsum [join $fs ""]]}
}
proc range {n} {
for {set i 1} {$i < $n} {incr i} {lappend result $i}
return $result
}
 
set smiths [lmap i [range 10000] {
if {![smith? $i]} continue
set i
}]
 
puts [lrange $smiths 0 12]...
puts ...[lrange $smiths end-12 end]
puts "([llength $smiths] total)"
 
Output:
4 22 27 58 85 94 121 166 202 265 274 319 346...
...9760 9778 9840 9843 9849 9861 9880 9895 9924 9942 9968 9975 9985
(376 total)

zkl[edit]

Uses the code (primeFactors) from Prime decomposition#zkl.

fcn smithNumbers(N=0d10_000){ // -->(Smith numbers to N)
[2..N].filter(fcn(n){
(pfs:=primeFactors(n)).len()>1 and
n.split().sum(0)==primeFactors(n).apply("split").flatten().sum(0)
})
}
sns:=smithNumbers();
sns.toString(*).println(" ",sns.len()," numbers");
Output:
L(4,22,27,58,85,94,121,166,202,265,274,319,346,355,378,382,391, ...
3091,3138,3168,3174,3226,3246,3258,3294,3345,3366,3390,3442,3505, ...
9942,9968,9975,9985) 376 numbers