A251753 - OEIS

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

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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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