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A103774 Number of ways to write n! as product of squarefree numbers. 2
1, 1, 2, 2, 6, 10, 42, 42, 82, 204, 1196, 1556, 10324, 34668, 104948, 104964, 873540, 1309396, 11855027, 25238220, 91193575, 453628255, 5002616219, 5902762219, 21142729523, 122981607092, 189706055368, 547296181656, 7291700021313, 14330422534833, 202498591157970 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) = A050320(A000142(n)).

LINKS

Table of n, a(n) for n=1..31.

Index entries for sequences related to factorial numbers.

EXAMPLE

n=5, 5! = 1*2*3*4*5 = 120 = 2 * 2 * 2 * 3 * 5: a(5)=#{2*2*2*3*5,2*2*2*15,2*2*6*5,2*2*30,2*2*3*10,2*6*10}=6.

MATHEMATICA

sub[w_, e_] := Block[{v=w}, v[[e]]--; v]; ric[w_, k_] := ric[w, k] = If[Max[w] == 0, 1, Block[{e, s, p = Flatten@ Position[Sign@w, 1]}, s = Select[ Prepend[#, First@p] & /@ Subsets[Rest@p], Total[1/2^#] <= k &]; Sum[ric[sub[w, e], Total[1/2^e]], {e, s}]]]; a[n_] := ric[ Sort[ Last /@ FactorInteger[n!]], 1]; Array[a, 22] (* Giovanni Resta, Sep 30 2019 *)

CROSSREFS

Cf. A000142, A005117, A050320, A103775.

Sequence in context: A076907 A260785 A153897 * A036052 A308260 A279212

Adjacent sequences:  A103771 A103772 A103773 * A103775 A103776 A103777

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 15 2005

EXTENSIONS

a(17)-a(18) from Amiram Eldar, Sep 30 2019

a(19)-a(31) from Giovanni Resta, Sep 30 2019

STATUS

approved

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Last modified February 27 10:15 EST 2020. Contains 332304 sequences. (Running on oeis4.)