A322672 a(n) = Product_{d|n} (pod(d)/d) where pod(k) is the product of the divisors of k (A007955).

1, 1, 1, 2, 1, 6, 1, 16, 3, 10, 1, 1728, 1, 14, 15, 1024, 1, 5832, 1, 8000, 21, 22, 1, 191102976, 5, 26, 81, 21952, 1, 24300000, 1, 1048576, 33, 34, 35, 470184984576, 1, 38, 39, 4096000000, 1, 130691232, 1, 85184, 91125, 46, 1, 64925062108545024, 7, 125000, 51

Offset: 1

Author

Jaroslav Krizek, Dec 23 2018

Keywords

• nonn

Examples

			For n = 6; a(6) = pod(1)/1 * pod(2)/2 * pod(3)/3 * pod(6)/6 = 1/1 * 2/2 * 3/3 * 36/6 = 6.
		

Crossrefs

Cf. A006881, A007955, A322671.

Programs

Magma

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

Mathematica

Array[Product[Apply[Times, Divisors@ d]/d, {d, Divisors@ #}] &, 51] (* Michael De Vlieger, Jan 19 2019 *)

PARI

a(n) = my(x=1); fordiv(n, d, x*=vecprod(divisors(d))/d); x; \\ Michel Marcus, Dec 23 2018

Formula

a(n) = n for n = 1 and squarefree semiprimes (A006881).