A128680 Numbers k such that k^3 divides 6^(k^2) + 1.

1, 7, 203, 1379, 11977, 39991, 577129, 2359469, 4780447, 6521291, 6640739, 9904979, 21511301, 28434413, 34050611, 113694413, 189117439, 222281549, 250163599, 282046373, 391803601, 941748059, 1269166759, 1308225583

Offset: 1

Author

Alexander Adamchuk, Mar 31 2007

Keywords

• hard
• nonn

Comments

7 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, A128681, A128682, A128683, A128684, A128685.

Programs

Mathematica

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

Extensions

More terms from Ryan Propper, Jan 13 2008