A128681 Numbers k such that k^3 divides 8^(k^2) + 1.

1, 3, 9, 57, 171, 1467, 13131, 27873, 32547, 97641, 249489, 261633, 784899, 1218897, 1255347, 2140353, 4971027, 8246019, 9961491, 12914001, 14913081, 15915483, 23159043, 23851593, 24738057, 29884473, 40666707, 83512353, 127938537

Offset: 1

Author

Alexander Adamchuk, Mar 31 2007

Keywords

• hard
• nonn

Comments

3 divides a(n) for n > 1.

Crossrefs

Cf. A127263 (numbers k such that k^3 divide 2^(k^2)+1).

Cf. A128677 (least k > p such that (k*p)^3 divides (p-1)^(k*p)^2+1, where p = prime(n) > 2).

Cf. A128678, A128679, A128680, A128682, A128683, A128684, A128685.

Programs

Mathematica

Select[Range[5*10^6], Mod[ 8^(#^2)+1, #^3]==0 &] (* G. C. Greubel, Jan 18 2018 *)

Extensions

More terms from Ryan Propper, Jan 13 2008