A127102 Numbers k such that k^2 divides 8^k-1.

1, 7, 889, 2359, 299593, 2033143, 13549249, 42931441, 100170217, 310935751, 685169191, 3606045247, 4566096913, 5452293007, 6620620783, 12721617559, 30987132463, 65576560063, 92349997537, 104785348087, 457967746369

Offset: 1

Author

Alexander Adamchuk, Jan 05 2007, Jan 07 2007

Keywords

• nonn

Comments

Subsequence of A014949.

a(5) = 299593 = (8^7-1)/7 is a repunit in base 8, 1111111(base 8). The first 5 listed terms of a(n) are terms of the finite sequence A003530: divisors of 8^7-1. [Corrected and edited by M. F. Hasler, Nov 21 2018]

Also a subsequence of A177908, see there for more comments on properties of terms of this sequence. - M. F. Hasler, Nov 21 2018

Crossrefs

Cf. A127100, A127101, A127103, A127104, A127105, A127106, A127107, A127092, A014949, A003530.

Programs

Mathematica

Select[Range[20000], IntegerQ[(PowerMod[8, #, #^2 ]-1)/#^2 ]&]

PARI

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

Extensions

More terms from Ryan Propper, Jan 05 2007

Terms a(12) onward from Max Alekseyev, May 06 2010