A127263 Numbers k such that k^3 divides 2^(k^2)+1.

1, 3, 57, 32547, 9961491, 297381939, 1338104811, 3942759027, 5688011361, 8920514307, 9146532873, 40253706489, 243640690617, 764039295291, 1127102902923, 1556475424971, 2251315404417, 3005607686883, 5222670270483

Offset: 1

Author

Max Alekseyev, Mar 27 2007, Mar 29 2007, Apr 18 2007

Keywords

• nonn

Comments

If k belongs to this sequence, then so does (2^(k^2)+1)/k^2.

From Alexander Adamchuk, May 14 2010: (Start)

3 divides a(n) for n>1.

19 divides a(n) for n>2. (End)

Links

• ArtOfProblemSolving forum, n^3 | (2^{n^2}+1)

Crossrefs

Cf. A006521, A093546, A093665, A136372, A128677.

Cf. A128678, A128679, A128680, A128681, A128682, A128683, A128684, A128685, A177813, A177814, A177816, A177817, A177818, A177819, A177820.

Programs

Mathematica

Select[Range[100000], Divisible[2^(#^2) + 1, #^3] &] (* Robert Price, Mar 23 2020 *)

Extensions

a(7) from Ryan Propper, Jan 01 2008

a(8)-a(19) from Max Alekseyev, May 14 2010