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A072082 Numbers divisible by the cube of the sum of their digits in base 10.

%I A072082 #25 Sep 08 2022 08:45:06
%S A072082 1,10,100,200,500,512,1000,2000,2401,4913,5000,5103,5120,5832,10000,
%T A072082 10206,11000,11200,11664,13122,14000,17576,19000,19683,20000,20412,
%U A072082 21141,23000,23328,24010,28000,29160,32000,37000,39366,40000,40824
%N A072082 Numbers divisible by the cube of the sum of their digits in base 10.
%C A072082 If k is a term, then 10 * k is a term. There are an infinite number of terms that are not divisible by 10. The numbers m = 24 * 10^(294 * k - 292) +1 are divisible by 7^3 = digsum(m)^3. Also, the numbers s = 491 * 10^(4624 * k - 4623) + 3, k >= 1, are divisible by 17^3 = digsum(s)^3. - _Marius A. Burtea_, Mar 18 2020
%H A072082 Donovan Johnson, <a href="/A072082/b072082.txt">Table of n, a(n) for n = 1..1000</a>
%e A072082 k=98415: sumdigits(98415)=27, q=98415=5*27*27*27.
%t A072082 sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^3; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]
%t A072082 Select[Range[50000],Divisible[#,Total[IntegerDigits[#]]^3]&] (* _Harvey P. Dale_, Mar 22 2016 *)
%o A072082 (Magma) [k:k in [1..41000]| k mod &+Intseq(k)^3 eq 0]; // _Marius A. Burtea_, Mar 18 2020
%o A072082 (PARI) is(n)=n%sumdigits(n)^3==0 \\ _Charles R Greathouse IV_, Mar 19 2020
%Y A072082 Cf. A055012, A005349, A003634, A072081, A072083.
%K A072082 base,nonn
%O A072082 1,2
%A A072082 _Labos Elemer_, Jun 14 2002