A280582 a(n) = the product of divisors of product of divisors of n.

1, 2, 3, 64, 5, 10077696, 7, 2097152, 729, 1000000000, 11, 2116471057875484488839167999221661362284396544, 13, 20661046784, 38443359375, 36028797018963968, 17, 52655678627806560751363688397557640770141543227981824, 19

Offset: 1

Author

Jaroslav Krizek, Jan 06 2017

Keywords

• nonn

Examples

			For n = 4; a(n) = product of divisors (1*2*4) = 1*2*4*8 = 64.
		

Crossrefs

Cf. A000040, A001597, A002808, A007955, A280581.

Programs

Magma

[&*[d: d in Divisors(&*[d: d in Divisors(n)])]: n in [1..100]]

Mathematica

Table[Nest[Times @@ Divisors@ # &, n, 2], {n, 19}] (* Michael De Vlieger, Jan 06 2017 *)

Formula

a(n) = A007955(A007955(n)).

For p = primes (A000040); a(p) = p.

For c = composites (A002808); a(c) = perfect powers of the form m^k where m > 1 and k >= 2 (terms of A001597).