A236329 a(n) = sigma(n,1) * sigma(n,2) * ... * sigma(n,n).

1, 15, 1120, 2929563, 38464354656, 80529415686720000, 538252697895729090560000, 1045011472134222568417452736171875, 14983270528936392555878952946810076508388237, 30023920804570215919584229032152609459437167079578240000

Offset: 1

Author

Colin Barker, Jan 22 2014

Keywords

• nonn

Comments

sigma(n, k) is the sum of the k-th powers of the divisors of n.

Examples

			a(4) = sigma(4,1)*sigma(4,2)*sigma(4,3)*sigma(4,4) = 7*21*73*273 = 2929563.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..35

Crossrefs

Cf. A236328.

Cf. A000203, A001157, A001158, A001159, A001160.

Programs

Maple

with(NumberTheory): seq(product(sigma[k](n), k = 1..n), n = 1..10); # Vaclav Kotesovec, Aug 20 2019

Mathematica

Table[Times@@DivisorSigma[Range[n],n],{n,10}] (* Harvey P. Dale, Oct 21 2017 *)

PARI

vector(12, n, prod(k=1, n, sigma(n, k)))

Formula

log(a(n)) ~ n*(n+1)*log(n)/2. - Vaclav Kotesovec, Aug 21 2019