A035163 Composite numbers k, not a power of 2, such that the E(k) == 1 (mod k), where E(k) is the k-th Euler number (A000364).

15, 91, 289, 319, 435, 561, 692, 703, 1016, 1105, 1369, 1495, 1729, 1885, 1891, 2105, 2465, 2701, 2755, 2821, 3367, 4371, 5551, 6409, 6601, 7456, 8224, 8569, 8695, 8911, 9088, 10585, 10621, 11305, 11849, 12121, 12403, 13981, 14065, 15051, 15841, 16471, 17104

Offset: 1

Author

Benoit Cloitre, Apr 06 2003

Keywords

• nonn

Crossrefs

Cf. A000364, A081730.

Programs

Mathematica

Select[Range[1000], CompositeQ[#] && #/2^IntegerExponent[#, 2] > 1 && Divisible[Abs[EulerE[2*#]] - 1, #] &] (* Amiram Eldar, Nov 26 2020 *)

PARI

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

Extensions

More terms from Hans Havermann, Apr 07 2003

a(23)-a(43) from Amiram Eldar, Nov 26 2020