A326577 a(n) = (2*n - 1) / A326478(2*n - 1).

1, 3, 5, 7, 3, 11, 13, 3, 17, 19, 3, 23, 5, 3, 29, 31, 3, 1, 37, 3, 41, 43, 15, 47, 7, 3, 53, 1, 3, 59, 61, 3, 5, 67, 3, 71, 73, 3, 1, 79, 3, 83, 5, 3, 89, 7, 3, 1, 97, 3, 101, 103, 15, 107, 109, 3, 113, 1, 3, 1, 11, 3, 5, 127, 3, 131, 7, 3, 137, 139, 3, 1, 5

Offset: 1

Author

Peter Luschny, Jul 16 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A326478, A326578, A027641/A027642 (Bernoulli).

Programs

Maple

A326577 := n -> (2*n - 1)/A326478(2*n - 1): seq(A326577(n), n=1..72);
db := n -> denom(bernoulli(n)): nb := n -> numer(bernoulli(n)):
a := n -> igcd(db(2*n-2), (2*n-1)*nb(2*n-2)): seq(a(n), n=1..72);

Mathematica

a[n_] := Module[{b =  BernoulliB[2*n -2]}, (2* n - 1) * Denominator[b] / ((2 * n - 1) * Denominator[(2 * n - 1) * b])]; Array[a, 100] (* Amiram Eldar, Apr 26 2024 *)

PARI

f(n) = n*denominator(n*bernfrac(n-1))/denominator(bernfrac(n-1)); \\ A326478
a(n) = (2*n-1)/f(2*n-1); \\ Michel Marcus, Jul 17 2019

Formula

If 2*n - 1 is prime then a(n) is prime.

a(n) = gcd((2*n-1)*N(2*n-2), D(2*n-2)), with N(k)/D(k) = B(k) the k-th Bernoulli number.