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A072083 Numbers divisible by the 4th power of the sum of their digits in base 10. 3
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 (list; graph; refs; listen; history; text; internal format)
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 >= 5, 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 A136877

Adjacent sequences:  A072080 A072081 A072082 * A072084 A072085 A072086

KEYWORD

base,nonn

AUTHOR

Labos Elemer, Jun 14 2002

STATUS

approved

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Last modified June 24 17:11 EDT 2021. Contains 345417 sequences. (Running on oeis4.)