A072083 Numbers divisible by the 4th power of the sum of their digits in base 10.

1, 10, 100, 1000, 2000, 2401, 5000, 10000, 13122, 20000, 24010, 50000, 100000, 110000, 131220, 140000, 190000, 200000, 230000, 234256, 240100, 280000, 320000, 370000, 390625, 400221, 410000, 460000, 500000, 512000, 550000, 614656, 640000

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, k = 7*a - 6, a >= 1, are divisible by 7^4 = digsum(m)^4. Also, the numbers s = 491 * 10^(4624*k - 4623) + 3, k = 17*u - 11, u >= 1, are divisible by 17^4 = digsum(s)^4. - Marius A. Burtea, Mar 19 2020

The numbers 2^A095412(n), n >= 6, are terms. - Marius A. Burtea, Apr 02 2020

Examples

			k=614656: sumdigits(614656)=28, q=1, since k=28*28*28*28.
		

Links

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

Crossrefs

Cf. A005349, A003634, A072081, A072082.

Programs

Magma

[k:k in [1..640000]| k mod &+Intseq(k)^4 eq 0]; // Marius A. Burtea, Mar 19 2020

Mathematica

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^4; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]
Select[Range[700000],Divisible[#,Total[IntegerDigits[ #]]^4]&] (* Harvey P. Dale, Jun 28 2011 *)

PARI

isok(m) = (m % sumdigits(m)^4) == 0; \\ Michel Marcus, Apr 02 2020