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

Author

Paul Curtz, Mar 10 2013

Keywords

• nonn

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).

Examples

			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.
		

Programs

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 *)

Formula

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

Extensions

More terms from Jean-François Alcover, Mar 15 2013