A177908 Integers n such that n^3 divides 8^(n^2) - 1.

1, 7, 889, 2359, 299593, 2033143, 13549249, 42931441, 100170217, 188097287, 233727361, 310935751, 685169191, 1515836567, 3606045247, 4566096913, 5452293007, 6620620783, 12721617559, 13162910047, 24088984969, 29683374847, 30987132463, 63388785719, 65576560063, 92349997537

Offset: 1

Author

Max Alekseyev, May 17 2010

Keywords

• nonn

Comments

Contains A127102 as a subsequence.

From M. F. Hasler, Nov 21 2018: (Start)

The first terms not in A127102 are a({10, 11, 14, 20, 21, 22, ...}) = {188097287, 233727361, 1515836567, 13162910047, 24088984969, 29683374847, ...}.

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)

Crossrefs

Cf. A129211, A129212, A177905, A177907, A177909, A177243, A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

Mathematica

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 *)

PARI

is(n)=Mod(8,n^3)^n^2==1 \\ M. F. Hasler, Nov 21 2018

Extensions

a(23)-a(26) from Giovanni Resta, Nov 23 2018