A081730 Numbers k such that the k-th Euler number == 1 (mod k).

1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 19, 23, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 64, 67, 71, 73, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Benoit Cloitre, Apr 06 2003

Keywords

• nonn

Comments

All primes and all powers of 2 are in the sequence. The composite terms that are not powers of 2 are in A035163.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2000

Crossrefs

Union of A035163 and A174090.

Cf. A000079, A000364, A065091, A069042.

Programs

Mathematica

Select[Range[250], Divisible[Abs[EulerE[2*#]] - 1, #] &] (* Amiram Eldar, Apr 22 2025 *)

PARI

a000364(n)=subst(bernpol(2*n+1), 'x, 1/4)*4^(2*n+1)*(-1)^(n+1)/(2*n+1);
lista(nn) = {for (n=1, nn, if (Mod(a000364(n), n) == 1, print1(n, ", ")););} \\ Michel Marcus, Apr 18 2015

Extensions

More terms from Weston Markham (weston.markham(AT)gmail.com), May 22 2005