A326578 a(n) = n^2*denominator(n*Bernoulli(n-1))/denominator(Bernoulli(n-1)) = n*A326478(n).

1, 2, 3, 16, 5, 36, 7, 64, 27, 100, 11, 144, 13, 196, 75, 256, 17, 324, 19, 400, 147, 484, 23, 576, 125, 676, 243, 784, 29, 900, 31, 1024, 363, 1156, 1225, 1296, 37, 1444, 507, 1600, 41, 1764, 43, 1936, 135, 2116, 47, 2304, 343, 2500, 867, 2704, 53, 2916, 3025

Offset: 1

Author

Peter Luschny, Jul 16 2019

Keywords

• nonn

Comments

Conjecture: If n is Carmichael then a(n) = n.

Are the fixed points of this sequence the numbers satisfying Korselt's criterion?

Links

• Peter Luschny, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A326478, A326579, A326577, A027641/A027642 (Bernoulli), A002997 (Carmichael), A324050 (Korselt).

Programs

Maple

A326578 := n -> n*A326478(n): seq(A326578(n), n=1..55);
db := n -> denom(bernoulli(n)): nb := n -> numer(bernoulli(n)):
a := n -> n^2/igcd(n*nb(n-1), db(n-1)): seq(a(n), n=1..55);

Mathematica

a[n_] := Module[{b =  BernoulliB[n - 1]}, n^2 * Denominator[n * b] / Denominator[b]]; Array[a, 60] (* Amiram Eldar, Apr 26 2024 *)

PARI

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

Formula

a(prime(n)) = prime(n).

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