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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

MATHEMATICA

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

PROG

(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