A306745 Even bisection of A318256.

1, 2, 6, 6, 10, 6, 210, 2, 30, 210, 110, 30, 546, 14, 30, 462, 1190, 6, 51870, 70, 2310, 2310, 322, 210, 6630, 286, 330, 798, 290, 30, 930930, 1430, 1122, 82110, 70, 330, 21111090, 38038, 390, 210, 536690, 39270, 7489482, 10010, 62790, 4470510, 687610, 462

Offset

0,2

Comments

The ratio sequence of a(n)/A006955(n) begins: 1,1,1,1,1,1,1,1,1,5,1,5,1,7,1,1,7,1,1,35, ...

This divisibility by A006955 was confirmed by Peter Luschny in the SeqFan mailing list.

Links

Jean-François Alcover, Table of n, a(n) for n = 0..1000

Formula

a(n) = (denominator of B(2n,x)) / (the squarefree kernel of 2n+1), where B(2n,x) is the 2n-th Bernoulli polynomial.

Mathematica

sfk[n_] := Times @@ FactorInteger[n][[All, 1]];
a[n_] := (BernoulliB[2 n, x] // Together // Denominator)/sfk[2 n + 1];
Table[a[n], {n, 0, 60}]

Crossrefs

Cf. A006955, A318256.

Sequence in context: A021978 A141377 A006955 * A196053 A063210 A114718

Adjacent sequences: A306742 A306743 A306744 * A306746 A306747 A306748

Keyword

nonn

Author

Jean-François Alcover and Paul Curtz, Mar 07 2019

Status

approved