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

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

Offset

1,2

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

Links

Table of n, a(n) for n=1..21.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A093171 A330295 A177908 * A269932 A352401 A252175

Adjacent sequences: A127099 A127100 A127101 * A127103 A127104 A127105

Keyword

nonn

Author

Alexander Adamchuk, Jan 05 2007, Jan 07 2007

Extensions

More terms from Ryan Propper, Jan 05 2007

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

Status

approved