A177909 Numbers k such that k^3 divides 9^(k^2) - 1.

1, 2, 4, 8, 10, 20, 40, 68, 82, 110, 136, 164, 220, 328, 340, 410, 440, 610, 680, 772, 820, 1010, 1210, 1220, 1510, 1544, 1640, 2020, 2420, 2440, 2530, 2788, 3020, 3740, 3860, 4040, 4510, 4840, 5060, 5576, 6040, 6710, 6806, 7004, 7370, 7480, 7720, 8020, 9020

Offset: 1

Author

Alexander Adamchuk, May 14 2010

Keywords

• nonn

Examples

			9^(2^2) - 1 = 6560, which is divisible by 2^3, so 2 is in the sequence.
9^(4^2) - 1 = 1853020188851840, which is divisible by 4^3, so 4 is in the sequence.
9^(6^2) - 1 = 22528399544939174411840147874772640, which is not divisible by 6, and certainly not by 6^3, so 6 is not in the sequence.
		

Links

• Robert Price, Table of n, a(n) for n = 1..446 (terms 1..119 from R. J. Mathar).

Crossrefs

Cf. A068382 (k divides 9^k-1), A127101 (k^2 divides 9^k-1).

Cf. A129211, A129212, A177905, A127106, A177907, A127102, A177909, A177243.

Cf. A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

Maple

A177909:=n->`if`(9^(n^2)-1 mod n^3 = 0,n,NULL): seq(A177909(n), n=1..1000); # Wesley Ivan Hurt, Oct 04 2014

Mathematica

Select[Range[100], Divisible[9^(#^2) - 1, #^3] &] (* Alonso del Arte, Oct 04 2014 *)