A229338 Product of products of elements of subsets of divisors of n.

1, 4, 9, 4096, 25, 2821109907456, 49, 281474976710656, 531441, 10000000000000000, 121, 39939223824273992215667642551956428337968885602521915290518994217942463316460321327052965050967304175616, 169, 2177953337809371136, 6568408355712890625, 1461501637330902918203684832716283019655932542976

Offset: 1

Author

Jaroslav Krizek, Sep 20 2013

Keywords

• nonn

Examples

			For n = 4; divisors of 4: {1, 2, 4}; subsets of divisors of n: {}, {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; product of products of elements of subsets = 1*1*2*4*2*4*8*8 = 4096.
		

Crossrefs

Cf. A229335 (sum of sums of the elements), A229336 (product of sums of the elements), A229337 (sum of products of the elements).

Programs

Mathematica

Table[Times@@Times@@@Subsets[Divisors[n]],{n,20}] (* Harvey P. Dale, Mar 05 2015 *)

Formula

Conjecture: a(n) = n^s(n); where s(n) = A057711(tau(n)) = A057711(A000005(n)) = tau(n)*2^(tau(n)-2).