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

1, 10, 100, 200, 500, 512, 1000, 2000, 2401, 4913, 5000, 5103, 5120, 5832, 10000, 10206, 11000, 11200, 11664, 13122, 14000, 17576, 19000, 19683, 20000, 20412, 21141, 23000, 23328, 24010, 28000, 29160, 32000, 37000, 39366, 40000, 40824

Offset: 1

Author

Labos Elemer, Jun 14 2002

Keywords

• base
• nonn

Comments

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

Examples

			k=98415: sumdigits(98415)=27, q=98415=5*27*27*27.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055012, A005349, A003634, A072081, A072083.

Programs

Magma

[k:k in [1..41000]| k mod &+Intseq(k)^3 eq 0]; // Marius A. Burtea, Mar 18 2020

Mathematica

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^3; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]
Select[Range[50000],Divisible[#,Total[IntegerDigits[#]]^3]&] (* Harvey P. Dale, Mar 22 2016 *)

PARI

is(n)=n%sumdigits(n)^3==0 \\ Charles R Greathouse IV, Mar 19 2020