A127101 Numbers k such that k^2 divides 9^k - 1.

1, 2, 4, 8, 10, 20, 40, 110, 136, 164, 220, 328, 440, 610, 680, 820, 1210, 1220, 1544, 1640, 2420, 2440, 2530, 4840, 5060, 5576, 6710, 7370, 7480, 7720, 9020, 10120, 11810, 13420, 13612, 14008, 14740, 18040, 18632, 19580

Offset: 1

Author

Alexander Adamchuk, Jan 05 2007

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3000 (terms 1..56 from R. J. Mathar)

Crossrefs

Subset of A068382 (numbers k such that k divides 9^k - 1).

Cf. A127100, A127102, A127103, A123104, A127105, A127106, A127107, A127092.

Programs

Mathematica

Select[Range[20000], IntegerQ[(PowerMod[9, #, #^2 ]-1)/#^2 ]&]

PARI

is(k) = Mod(9, k^2)^k == 1; \\ Amiram Eldar, May 21 2024