A057642 (Product k^k) * (Sum 1/k^k) where both the sum and product are over those positive integers k that divide n.

1, 5, 28, 1284, 3126, 6485292, 823544, 21541946368, 10847773719, 156290000012500, 285311670612, 14847746691430172786688, 302875106592254, 45756121633729931379676, 38327538543365478600000, 397378771500072999738379599872, 827240261886336764178

Offset: 1

Author

Leroy Quet, Oct 11 2000

Keywords

• nonn

Examples

			The positive divisors of 4 are 1, 2, 4. So a(4) = 1^1 *2^2 *4^4 *(1/1^1 +1/2^2 +1/4^4) = 1284.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200

Programs

Maple

with(numtheory):
a:= n-> (l-> mul(k^k, k=l)*add(1/k^k, k=l))(divisors(n)):
seq(a(n), n=1..20);  # Alois P. Heinz, May 22 2015

Mathematica

a[n_] := Function[l, Product[k^k, {k, l}] * Sum[1/k^k, {k, l}]] @ Divisors[n]; Array[a, 20] (* Jean-François Alcover, Mar 23 2017 *)