A163087 Product{k|n} k$. Here '$' denotes the swinging factorial function (A056040).

1, 1, 2, 6, 12, 30, 240, 140, 840, 3780, 15120, 2772, 221760, 12012, 960960, 9266400, 10810800, 218790, 7351344000, 923780, 16761064320, 3259095840, 3910915008, 16224936, 41977154419200, 2028117000, 249864014400

Offset: 0

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn

Examples

			The set of positive divisors of 3 is {1,3}. Thus a(3) = 1$ * 3$ = 1 * 6 = 6.
		

Links

• Peter Luschny, Swinging Primes.

Crossrefs

Cf. A098710, A163088, A163089.

Programs

Maple

a := proc(n) local i; mul(i,i=map(swing,numtheory[divisors](n))) end:

Mathematica

sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; a[0] = 1; a[n_] := Product[sf[k], {k, Divisors[n]}]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Jul 26 2013 *)