A098375 (1/p)*abs(p*(p^(p-1)-1)*B(p-1)-1) when p runs through the primes and B(k) denotes the k-th Bernoulli's number.

1, 1, 21, 2801, 1964956409, 5897061106093, 345112805910366790769, 5724003102153474225966281, 5621496960287976955328551429580241, 2417009997194019381479073094599560492013039757981, 331241570655571671768537062318886722305299290781512129

Offset: 1

Author

Benoit Cloitre, Oct 26 2004

Keywords

• nonn

Comments

Conjecture: p is an odd prime iff p divides p*(p^(p-1)-1)*B(p-1)-1. Seems to be the equivalent (with integer moduli) to Agoh's conjecture (which involves rational moduli).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..58
• Eric Weisstein's World of Mathematics, Agoh's Conjecture.

Crossrefs

Cf. A027641, A027642, A089655.

Programs

Mathematica

f[p_] := Abs[p * (p^(p-1)-1) * BernoulliB[p-1] - 1]; Table[f[p]/p, {p, Prime[Range[10]]}] (* Amiram Eldar, Apr 26 2025 *)

PARI

a(n)=(1/prime(n))*(prime(n)*(prime(n)^(prime(n)-1)-1)*bernfrac(prime(n)-1)-1);