A277174 a(n) = Product_{i=1..n} i*rad(i) where rad(n) = A007947(n).

1, 1, 4, 36, 288, 7200, 259200, 12700800, 203212800, 5486745600, 548674560000, 66389621760000, 4780052766720000, 807828917575680000, 158334467844833280000, 35625255265087488000000, 1140008168482799616000000, 329462360691529089024000000

Offset: 0

Author

Peter Luschny, Oct 02 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..268

Crossrefs

Cf. A007947, A048803.

Programs

Maple

A277174 := proc(n) local rad, i;
rad := n -> mul(k, k in numtheory:-factorset(n));
mul(i * rad(i), i=1..n) end:
seq(A277174(i), i=0..17);

Mathematica

Table[Product[i Last@ Select[Divisors@ i, SquareFreeQ], {i, n}], {n, 0, 17}] (* Michael De Vlieger, Oct 02 2016 *)

PARI

a(n) = prod(i=1, n, i*factorback(factorint(i)[, 1])); \\ Michel Marcus, Oct 03 2016

Formula

a(n) = n! * A048803(n). - Robert Israel, Oct 02 2016