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A251753 n!/pp, where pp is the largest perfect power (A001597) which divides n!. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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

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]

CROSSREFS

Cf. A000142, A001597, A090630.

Sequence in context: A094300 A055773 A111866 * A072155 A094299 A304537

Adjacent sequences:  A251750 A251751 A251752 * A251754 A251755 A251756

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Dec 07 2014

STATUS

approved

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)