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%I #9 Feb 19 2021 04:22:50
%S 1,2,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,23,24,25,27,29,31,32,36,37,
%T 41,43,44,45,47,48,53,54,59,61,64,67,71,72,73,75,79,81,83,89,95,96,97,
%U 101,103,107,108,109,113,125,127,128,131,133,135,137,139,144,149,151
%N Numbers k such that k divides 5^k - 3^k - 2^k = A130072(k).
%C All primes are the terms of a(n). Quotients A130072(p)/p for p = Prime(n) are listed in A130075(n) = {6,30,570,10830,4422630,93776970,44871187170,1003806502230,...}. p^(k+1) divides A130072(p^k) for prime p = {2,3,5,19} = A130076(n) and all k>0. Nonprimes n such that n divides A130072(n) are listed in A130074(n) = {1,4,6,8,9,12,15,16,18,24,25,27,32,36,44,45,48,54,64,72,75,81,95,96,...} which apparently include all powers p^k of primes p = {2,3,5,19} for k>1 and all powers of numbers of the form 2^k*3^m, 3^k*5^m, 5^k*19^m.
%H Amiram Eldar, <a href="/A130073/b130073.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[1000],IntegerQ[(PowerMod[5,#,# ]-PowerMod[3,#,# ]-PowerMod[2,#,# ])/# ]&]
%o (PARI) is(n)=Mod(5,n)^n==Mod(3,n)^n+Mod(2,n)^n \\ _Charles R Greathouse IV_, Nov 04 2016
%Y Cf. A130072, A130074, A130075, A130076.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, May 06 2007
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