A179215 Product of squarefree numbers less than n+1.

1, 1, 2, 6, 6, 30, 180, 1260, 1260, 1260, 12600, 138600, 138600, 1801800, 25225200, 378378000, 378378000, 6432426000, 6432426000, 122216094000, 122216094000, 2566537974000, 56463835428000, 1298668214844000, 1298668214844000, 1298668214844000, 33765373585944000

Offset: 0

Author

Reinhard Zumkeller, Jul 05 2010

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..680

Crossrefs

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

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

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      a(n-1)*`if`(issqrfree(n), n, 1))
    end:
seq(a(n), n=0..27);  # Alois P. Heinz, Sep 20 2021

Mathematica

With[{sfnos=Select[Range[50],SquareFreeQ]},Table[Times@@Select[sfnos, #Harvey P. Dale, Jun 13 2011 *)

PARI

a(n) = prod(k=1, n, if (issquarefree(k), k, 1)); \\ Michel Marcus, Sep 20 2021

PARI

a(n) = my(p=1); forsquarefree(x=1, n, p*=x[1]); p; \\ Michel Marcus, Sep 20 2021

Formula

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

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

Subsequence of A025487.

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

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

Extensions

Definition corrected by Harvey P. Dale, Jun 13 2011