A127104 Numbers k such that k^2 divides 4^k-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, 262275447, 300510651, 314353263, 335873559, 349662369

Offset: 1

Author

Alexander Adamchuk, Jan 05 2007

Keywords

• nonn

Comments

From Alexander Adamchuk, Jan 11 2007: (Start)

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, ...}. (End)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..56

Crossrefs

Cf. A127100, A127101, A127102, A127103, A127105, A127106, A127107, A127092.

Subset of A014945 (numbers k such that k divides 4^nk-1).

Programs

Mathematica

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

PARI

is(k) = Mod(4, k^2)^k == 1; \\ Amiram Eldar, May 25 2024

Extensions

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

a(27)-a(31) from Amiram Eldar, May 25 2024