A251753 n!/pp, where pp is the largest perfect power (A001597) which divides n!.

1, 1, 2, 6, 3, 15, 5, 35, 70, 70, 7, 77, 231, 3003, 858, 1430, 1430, 24310, 12155, 230945, 46189, 230945, 176358, 4056234, 676039, 676039, 104006, 312018, 44574, 1292646, 1077205, 33393355, 66786710, 2203961430, 64822395, 90751353, 90751353, 3357800061, 353452638, 1531628098, 3829070245, 156991880045

Offset: 0

Author

Robert G. Wilson v, Dec 07 2014

Keywords

• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000142, A001597, A090630.

Programs

Mathematica

perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; f[n_] := Block[{d = Divisors[n!], k = 1},  While[ ! perfectPowerQ[ d[[-k]]], k++]; n!/d[[-k]]]; Array[f, 41, 0] (* or *)
f[n_] := Block[{fi = FactorInteger[n!]}, n!/Times @@ (#1[[1]] ^ (2 Quotient[#1[[2]],2])&) /@ fi]; f[4] = 3; f[5] = 15; f[21] = 230945; Array[f, 40]

Formula

If p is prime, then a(p) = p*a(p-1).

a(n) = n! / A090630(n). - Joerg Arndt, Dec 08 2014