A163088 -id:A163088 - cp's OEIS frontend

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

Peter Luschny, Jul 21 2009

nonn

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

Peter Luschny, Swinging Primes.

Cf. A098710, A163088, A163089.

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

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 *)

A163089 n! / (Product{k|n} k$). Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 3, 36, 48, 96, 240, 14400, 2160, 518400, 90720, 141120, 1935360, 1625702400, 870912, 131681894400, 145152000, 15676416000, 287400960000, 1593350922240000, 14780620800, 7648084426752000, 1614043791360000

Offset: 0

Peter Luschny, Jul 21 2009

nonn

Peter Luschny, Swinging Primes.

Cf. A163087, A163088.

Maple
```
a := n -> n! / A163087(n):
```

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

cp's OEIS Frontend

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

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