%I #15 Aug 21 2019 11:13:18

%S 1,15,1120,2929563,38464354656,80529415686720000,

%T 538252697895729090560000,1045011472134222568417452736171875,

%U 14983270528936392555878952946810076508388237,30023920804570215919584229032152609459437167079578240000

%N a(n) = sigma(n,1) * sigma(n,2) * ... * sigma(n,n).

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

%H Vaclav Kotesovec, <a href="/A236329/b236329.txt">Table of n, a(n) for n = 1..35</a>

%F log(a(n)) ~ n*(n+1)*log(n)/2. - _Vaclav Kotesovec_, Aug 21 2019

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

%p with(NumberTheory): seq(product(sigma[k](n), k = 1..n), n = 1..10); # _Vaclav Kotesovec_, Aug 20 2019

%t Table[Times@@DivisorSigma[Range[n],n],{n,10}] (* _Harvey P. Dale_, Oct 21 2017 *)

%o (PARI) vector(12, n, prod(k=1, n, sigma(n, k)))

%Y Cf. A236328.

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

%K nonn

%O 1,2

%A _Colin Barker_, Jan 22 2014