A127104 Numbers n such that n^2 divides 4^n-1.

1, 3, 21, 903, 2667, 7077, 113799, 114681, 304311, 389193, 898779, 932799, 4893357, 6099429, 8131683, 8776257, 14452473, 38350263, 38647497, 40647747, 49427511, 99583113, 118465473, 128794323, 131158041, 152643813

Offset

1,2

Comments

a(n) is a subset of A014945(n) = {1, 3, 9, 21, 27, 63, 81, 147, 171, 189, 243, 441, 513, 567, 657, 729, ...} Numbers n such that n divides 4^n-1.

3 divides a(n) for n>1. 7 divides a(n) for n>2. 43 divides a(n) for n = {4,8,9,10,12,13,16,...}. 127 divides a(n) for n = {5,8,11,14,15,17,...}. Prime factors of a(n) in order of their appearance in a(n) are {3,7,43,127,337,5419,431,1033,5419,2287,3049,9719,...}. - Alexander Adamchuk, Jan 11 2007

Links

Table of n, a(n) for n=1..26.

Mathematica

Select[Range[30000], IntegerQ[(PowerMod[4, #, #^2 ]-1)/#^2 ]&]

Crossrefs

Cf. A127100, A127101, A127102, A127103, A127105, A127106, A127107, A127092. Cf. A014945 = numbers n such that n divides 4^n-1.

Sequence in context: A057600 A162924 A079269 * A176430 A340505 A327037

Adjacent sequences: A127101 A127102 A127103 * A127105 A127106 A127107

Keyword

nonn

Author

Alexander Adamchuk, Jan 05 2007

Extensions

More terms from Ryan Propper and Alexander Adamchuk, Jan 05 2007

Status

approved