A214867 Quotients of (first) primorial numbers and denominators of Bernoulli numbers B 0, B 1, B 2, B 4, B 6,... .

1, 1, 1, 1, 5, 77, 455, 187, 1616615, 437437, 8107385, 607759061, 53773464745, 111446982977, 2180460221945005, 706769865044243, 2275461421392965, 3770118333635711057, 19548063559901161830545, 4094603218587147211, 92990138354449826827902565

Offset

0,5

Comments

a(2*n+4) is divisible by 5 (because A006954(n+2)=6,30,42,30,... is divisible by A165734(n)=period of length 2: repeat 6,30).

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A002110(n)/A006954(n).

Example

a(0) = 1/1, a(1)= 2/2, a(2) = 6/6, a(3) = 30/30, a(4) =210/42=5.
By product (see A080092):
1,
1,
1,
1,
5,
7  * 11,
5  *  7 *13,
11 * 17,
5  *  7 *11 *13 *17 *19,
7  * 11 *13 *19 *23,
5  * 11 *13 *17 *23 *29,
7  * 13 *17 *19 *23 *29 *31,
5  *  7 *11 *13 *17 *19 *29 *31 *37.

Mathematica

a[n_] := Product[ Prime[k], {k, 1, n}] / Denominator[ BernoulliB[2*n-2] ]; a[0] = a[1] = 1; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 15 2013 *)

Crossrefs

Sequence in context: A001513 A028556 A364713 * A330999 A331000 A039753

Adjacent sequences: A214864 A214865 A214866 * A214868 A214869 A214870

Keyword

nonn

Author

Paul Curtz, Mar 10 2013

Extensions

More terms from Jean-François Alcover, Mar 15 2013

Status

approved