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A103774 Number of ways to write n! as product of squarefree numbers. 2

%I

%S 1,1,2,2,6,10,42,42,82,204,1196,1556,10324,34668,104948,104964,873540,

%T 1309396,11855027,25238220,91193575,453628255,5002616219,5902762219,

%U 21142729523,122981607092,189706055368,547296181656,7291700021313,14330422534833,202498591157970

%N Number of ways to write n! as product of squarefree numbers.

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

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

%e 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.

%t 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 *)

%Y Cf. A000142, A005117, A050320, A103775.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Feb 15 2005

%E a(17)-a(18) from _Amiram Eldar_, Sep 30 2019

%E a(19)-a(31) from _Giovanni Resta_, Sep 30 2019

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)