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Product of squarefree numbers less than n+1.
9

%I #21 Sep 20 2021 04:58:29

%S 1,1,2,6,6,30,180,1260,1260,1260,12600,138600,138600,1801800,25225200,

%T 378378000,378378000,6432426000,6432426000,122216094000,122216094000,

%U 2566537974000,56463835428000,1298668214844000,1298668214844000,1298668214844000,33765373585944000

%N Product of squarefree numbers less than n+1.

%H G. C. Greubel, <a href="/A179215/b179215.txt">Table of n, a(n) for n = 0..680</a>

%F a(n) = Product_{k=1..n} k^A008966(k).

%F A001221(a(n)) = A000720(n).

%F Subsequence of A025487.

%F A034386(n) <= a(n) <= A000142(n).

%F A179214(n) = a(2*n)/a(n-1) for n>0.

%p a:= proc(n) option remember; `if`(n=0, 1,

%p a(n-1)*`if`(issqrfree(n), n, 1))

%p end:

%p seq(a(n), n=0..27); # _Alois P. Heinz_, Sep 20 2021

%t With[{sfnos=Select[Range[50],SquareFreeQ]},Table[Times@@Select[sfnos, #<n+1&],{n,0,30}]] (* _Harvey P. Dale_, Jun 13 2011 *)

%o (PARI) a(n) = prod(k=1, n, if (issquarefree(k), k, 1)); \\ _Michel Marcus_, Sep 20 2021

%o (PARI) a(n) = my(p=1); forsquarefree(x=1, n, p*=x[1]); p; \\ _Michel Marcus_, Sep 20 2021

%Y Cf. A013928, A066779, A005117, A008966, A179214.

%Y Cf. A000142, A000720, A001221, A025487, A034386.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Jul 05 2010

%E Definition corrected by _Harvey P. Dale_, Jun 13 2011