cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A280355 Numbers that are divisible by the sum of their digits and for which the sum of digits equals the product of digits.

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%I A280355 #19 Feb 16 2025 08:33:39
%S A280355 1,2,3,4,5,6,7,8,9,132,312,4112,11133,11313,11331,13113,13131,13311,
%T A280355 22112,31113,31131,31311,33111,111216,111612,112116,116112,121116,
%U A280355 161112,211116,611112,1111712,11111232,11112132,11112312,11113212,11118112,11121132,11121312,11123112,11131212,11132112
%N A280355 Numbers that are divisible by the sum of their digits and for which the sum of digits equals the product of digits.
%H A280355 Chai Wah Wu, <a href="/A280355/b280355.txt">Table of n, a(n) for n = 1..10000</a>
%H A280355 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarshadNumber.html">Harshad Numbers</a>
%e A280355 132 is in the sequence because 1 + 3 + 2 = 1*3*2 = 6 and 6 divides 132.
%t A280355 Select[Range[11300000], Divisible[#1, (Plus @@ IntegerDigits[#1])] && (Plus @@ IntegerDigits[#1]) == (Times @@ IntegerDigits[#1]) &]
%t A280355 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 A280355 (PARI) isok(n) = (d=digits(n)) && ((n % vecsum(d)) == 0) && (vecsum(d) == prod(k=1, #d, d[k])); \\ _Michel Marcus_, Jan 02 2017
%Y A280355 Intersection of A005349 and A034710.
%Y A280355 Cf. A038186.
%K A280355 nonn,base,easy
%O A280355 1,2
%A A280355 _Ilya Gutkovskiy_, Jan 01 2017