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

1,2

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

Links

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

Example

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

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 *)

Prog

(Magma) [k:k in [1..41000]| k mod &+Intseq(k)^3 eq 0]; // Marius A. Burtea, Mar 18 2020
(PARI) is(n)=n%sumdigits(n)^3==0 \\ Charles R Greathouse IV, Mar 19 2020

Crossrefs

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

Sequence in context: A367593 A206983 A207841 * A078259 A101655 A043216

Adjacent sequences: A072079 A072080 A072081 * A072083 A072084 A072085

Keyword

base,nonn

Author

Labos Elemer, Jun 14 2002

Status

approved