A089655 -id:A089655 - cp's OEIS frontend

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

Benoit Cloitre, Oct 26 2004

nonn

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).

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

Cf. A027641, A027642, A089655.

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 *)

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

A110841 a(n) is the number of prime factors, with multiplicity, of abs(A014509(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 2, 7, 7, 2, 2, 4, 3, 3, 7, 1, 6, 4, 5, 14, 4, 9, 5, 10, 3, 11, 2, 5, 3, 7, 11, 5, 3, 4, 15, 6, 5, 19, 10, 6, 13, 15, 5, 10, 5, 5, 6, 7, 5, 15, 7, 5, 2, 13, 4, 3, 10, 5, 9, 7, 5, 4, 9, 5, 4, 1, 7, 4, 4, 5, 3, 11, 13, 10, 5, 5, 7, 6

Offset: 0

Jonathan Vos Post, Sep 16 2005

			a(10) = 2 because A014509(10) = 529 = 23^2.
a(8) = a(19) = 1 since A014509(8) and A014509(19) are prime.

Sean A. Irvine, Table of n, a(n) for n = 0..91

Cf. A001222, A073276, A075178, A076547, A076549, A079294, A083687, A084217, A085092, A085737, A089170, A089644, A089655.

a(n) = my(b=bernfrac(2*n), c=floor(abs(b))*sign(b)); if (c==0, 0, bigomega(c)); \\ Michel Marcus, Mar 29 2020

a(n) = A001222(abs(A014509(n))).

More terms from Michel Marcus, Mar 29 2020
a(51)-a(65) from Jinyuan Wang, Apr 02 2020
More terms from Sean A. Irvine, Jul 29 2024

cp's OEIS Frontend

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.

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A110841 a(n) is the number of prime factors, with multiplicity, of abs(A014509(n)).

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cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A110841 a(n) is the number of prime factors, with multiplicity, of abs(A014509(n)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions

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.