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%I #7 Feb 19 2021 04:22:19
%S 1,4,6,8,9,12,15,16,18,24,25,27,32,36,44,45,48,54,64,72,75,81,95,96,
%T 108,125,128,133,135,144,162,175,192,216,225,243,256,264,288,324,325,
%U 361,375,384,405,432,475,486,512,561,576,594,618,625,648,675,704,729,768
%N Nonprimes k such that k divides 5^k - 3^k - 2^k = A130072(k).
%C Numbers k such that k divides A130072(k) are listed in A130073(n) = {1,2,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,23,24,25,27,29,31,32,36,37,41,43,...}, which includes all primes. a(n) includes nonprimes in A130073(n). p^(k+1) divides A130072(p^k) for prime p = {2,3,5,19} = A130076(n) and all k>0. It appears that a(n) includes 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="/A130074/b130074.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[10000],!PrimeQ[ # ]&&IntegerQ[(PowerMod[5,#,# ]-PowerMod[3,#,# ]-PowerMod[2,#,# ])/# ]&]
%Y Cf. A130072, A130073, A130075, A130076.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, May 06 2007
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