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A123091 Numbers k such that k divides 5^k - 5.

%I A123091 #8 Jul 25 2021 02:39:51
%S A123091 1,2,3,4,5,7,10,11,13,15,17,19,20,23,29,31,37,41,43,47,53,59,61,65,67,
%T A123091 71,73,79,83,89,97,101,103,107,109,113,124,127,131,137,139,149,151,
%U A123091 157,163,167,173,179,181,190,191,193,197,199,211,217,223,227,229,233,239
%N A123091 Numbers k such that k divides 5^k - 5.
%C A123091 All primes are the terms of a(n). Nonprimes in a(n) are listed in A122782(n) = {1,4,10,15,20,65,124,190,217,310,435,561,781,...}. All pseudoprimes to base 5 are the terms of a(n). They are listed in A005936(n) = {4,124,217,561,781,...}. Numbers n up to 10^6 such that n divides 5^n + 5 are {1,2,5,6,10,30,70,1565,2806,3126,51670,58290,214405,285286,378258}.
%H A123091 Amiram Eldar, <a href="/A123091/b123091.txt">Table of n, a(n) for n = 1..10000</a>
%t A123091 Select[Range[1000], IntegerQ[(PowerMod[5,#,# ]-5)/# ]&]
%o A123091 (PARI) is(n)=Mod(5,n)^n==5 \\ _Charles R Greathouse IV_, Nov 04 2016
%Y A123091 Cf. A122782 (nonprimes n such that 5^n==5 (mod n)).
%Y A123091 Cf. A005936 (pseudoprimes to base 5).
%Y A123091 Cf. A067946 (numbers n such that n divides 5^n-1).
%Y A123091 Cf. A015951 (numbers n such that n | 5^n + 1).
%K A123091 nonn
%O A123091 1,2
%A A123091 _Alexander Adamchuk_, Nov 04 2006