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 A177908 Integers n such that n^3 divides 8^(n^2) - 1. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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) LINKS 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 *) PROG (PARI) is(n)=Mod(8, n^3)^n^2==1 \\ M. F. Hasler, Nov 21 2018 CROSSREFS Cf. A129211, A129212, A177905, A177907, A177909, A177243, A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920. Sequence in context: A332187 A093171 A330295 * A127102 A269932 A352401 Adjacent sequences: A177905 A177906 A177907 * A177909 A177910 A177911 KEYWORD nonn AUTHOR Max Alekseyev, May 17 2010 EXTENSIONS a(23)-a(26) from Giovanni Resta, Nov 23 2018 STATUS approved

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Last modified March 22 18:15 EDT 2023. Contains 361432 sequences. (Running on oeis4.)