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

1,2

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, 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

Links

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

Example

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

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 *)

Prog

(Magma) [k:k in [1..640000]| k mod &+Intseq(k)^4 eq 0]; // Marius A. Burtea, Mar 19 2020
(PARI) isok(m) = (m % sumdigits(m)^4) == 0; \\ Michel Marcus, Apr 02 2020

Crossrefs

Cf. A005349, A003634, A072081, A072082.

Sequence in context: A136863 A031201 A228989 * A029793 A233453 A358442

Adjacent sequences: A072080 A072081 A072082 * A072084 A072085 A072086

Keyword

base,nonn

Author

Labos Elemer, Jun 14 2002

Status

approved