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Numbers that are divisible by the sum of their digits and for which the sum of digits equals the product of digits.
1

%I #18 Nov 02 2024 14:19:06

%S 1,2,3,4,5,6,7,8,9,132,312,4112,11133,11313,11331,13113,13131,13311,

%T 22112,31113,31131,31311,33111,111216,111612,112116,116112,121116,

%U 161112,211116,611112,1111712,11111232,11112132,11112312,11113212,11118112,11121132,11121312,11123112,11131212,11132112

%N Numbers that are divisible by the sum of their digits and for which the sum of digits equals the product of digits.

%H Chai Wah Wu, <a href="/A280355/b280355.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarshadNumber.html">Harshad Numbers</a>

%e 132 is in the sequence because 1 + 3 + 2 = 1*3*2 = 6 and 6 divides 132.

%t Select[Range[11300000], Divisible[#1, (Plus @@ IntegerDigits[#1])] && (Plus @@ IntegerDigits[#1]) == (Times @@ IntegerDigits[#1]) &]

%t nQ[n_]:=With[{idn=IntegerDigits[n]},Mod[n,Total[idn]]==0&&Total[idn]==Times@@idn]; Select[Range[112*10^5],nQ] (* _Harvey P. Dale_, Nov 02 2024 *)

%o (PARI) isok(n) = (d=digits(n)) && ((n % vecsum(d)) == 0) && (vecsum(d) == prod(k=1, #d, d[k])); \\ _Michel Marcus_, Jan 02 2017

%Y Intersection of A005349 and A034710.

%Y Cf. A038186.

%K nonn,base,easy,changed

%O 1,2

%A _Ilya Gutkovskiy_, Jan 01 2017