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A229338 Product of products of elements of subsets of divisors of n. 4
1, 4, 9, 4096, 25, 2821109907456, 49, 281474976710656, 531441, 10000000000000000, 121, 39939223824273992215667642551956428337968885602521915290518994217942463316460321327052965050967304175616, 169, 2177953337809371136, 6568408355712890625, 1461501637330902918203684832716283019655932542976 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A168139 A258660 A260305 * A111443 A299118 A276272

Adjacent sequences:  A229335 A229336 A229337 * A229339 A229340 A229341

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Sep 20 2013

STATUS

approved

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Last modified March 28 14:56 EDT 2020. Contains 333089 sequences. (Running on oeis4.)