A072083 - OEIS

%I #32 Nov 25 2022 22:26:20

%S 1,10,100,1000,2000,2401,5000,10000,13122,20000,24010,50000,100000,

%T 110000,131220,140000,190000,200000,230000,234256,240100,280000,

%U 320000,370000,390625,400221,410000,460000,500000,512000,550000,614656,640000

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

%C 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

%C The numbers 2^A095412(n), n >= 6, are terms. - _Marius A. Burtea_, Apr 02 2020

%H Donovan Johnson, <a href="/A072083/b072083.txt">Table of n, a(n) for n = 1..1000</a>

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

%t sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^4; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]

%t Select[Range[700000],Divisible[#,Total[IntegerDigits[ #]]^4]&] (* _Harvey P. Dale_, Jun 28 2011 *)

%o (Magma) [k:k in [1..640000]| k mod &+Intseq(k)^4 eq 0]; // _Marius A. Burtea_, Mar 19 2020

%o (PARI) isok(m) = (m % sumdigits(m)^4) == 0; \\ _Michel Marcus_, Apr 02 2020

%Y Cf. A005349, A003634, A072081, A072082.

%K base,nonn

%O 1,2

%A _Labos Elemer_, Jun 14 2002