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%I #12 Nov 23 2018 05:25:46
%S 1,7,889,2359,299593,2033143,13549249,42931441,100170217,188097287,
%T 233727361,310935751,685169191,1515836567,3606045247,4566096913,
%U 5452293007,6620620783,12721617559,13162910047,24088984969,29683374847,30987132463,63388785719,65576560063,92349997537
%N Integers n such that n^3 divides 8^(n^2) - 1.
%C Contains A127102 as a subsequence.
%C From _M. F. Hasler_, Nov 21 2018: (Start)
%C The first terms not in A127102 are a({10, 11, 14, 20, 21, 22, ...}) = {188097287, 233727361, 1515836567, 13162910047, 24088984969, 29683374847, ...}.
%C The listed terms are all squarefree, and all but the first two terms appear to be divisible by either a(3) = 7*127 or a(4) = 7*337. Are there exceptions to these properties? (End)
%t Select[Range[2 10^5], IntegerQ[(8^(#^2) - 1) / #^3] &] (* or *) Select[Range[2 10^6], IntegerQ[(PowerMod[8, #, #^2] - 1) / #^3] &] (* _Vincenzo Librandi_, Nov 23 2018 *)
%o (PARI) is(n)=Mod(8,n^3)^n^2==1 \\ _M. F. Hasler_, Nov 21 2018
%Y Cf. A129211, A129212, A177905, A177907, A177909, A177243, A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.
%K nonn
%O 1,2
%A _Max Alekseyev_, May 17 2010
%E a(23)-a(26) from _Giovanni Resta_, Nov 23 2018
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