A093546 Numbers n such that n divides 2^n^2 + 1.

1, 3, 9, 27, 57, 81, 171, 243, 513, 729, 1083, 1467, 1539, 2187, 3249, 4401, 4617, 6561, 9747, 13203, 13851, 19683, 20577, 27873, 29241, 32547, 39393, 39609, 41553, 59049, 61731, 83619, 87723, 97641, 118179, 118827, 124659, 177147, 185193, 239121

Offset: 1

Author

Farideh Firoozbakht, Mar 31 2004

Keywords

• nonn

Comments

This sequence is closed under multiplication. A006521 is a subsequence of this sequence. A006521 is also closed under multiplication. In fact if m is even and k is a natural number then the sequence "n divides m^n^k + 1" is a subsequence of the sequence "n divides m^n^(k+1)+ 1" and both are closed under multiplication.

"Closed under multiplication" means that if x and y are terms then so is x*y.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..415

Crossrefs

Cf. A006521, A067945, A093547.

Programs

Mathematica

Select[ Range[250857], PowerMod[2, #^2, # ] == # - 1 &] (* Robert G. Wilson v, Apr 02 2004 *)

PARI

is(n)=Mod(2,n)^n^2==-1 \\ Charles R Greathouse IV, Aug 01 2016

Extensions

Corrected and extended by Robert G. Wilson v, Apr 02 2004