A129364 a(n) = Product_{k = 1..n} A066841(k).

1, 2, 6, 96, 480, 207360, 1451520, 2972712960, 722369249280, 5778953994240000, 63568493936640000, 9111096278347394580480000, 118444251618516129546240000, 10400352846118664303196241920000

Offset: 1

Author

Peter Bala, Apr 11 2007

Keywords

• nonn
• easy

Comments

Conjecture: a(n) divides A092287(n) for all n - see comments in A129365.

Crossrefs

Cf. A007955, A066841, A092143, A092287, A129365.

Programs

Mathematica

Table[Product[Floor[n/k]!^k, {k, 1, n}], {n, 1, 15}] (* Vaclav Kotesovec, Jun 24 2021 *)
Table[Product[k^(Floor[n/k]*(1 + Floor[n/k])/2), {k, 1, n}], {n, 1, 15}] (* Vaclav Kotesovec, Jun 24 2021 *)

PARI

a(n) = prod(k=1, n, k^((n\k) * (1 + n\k) \ 2)); \\ Daniel Suteu, Sep 12 2018

Formula

a(n) = Product_{k = 1..n} Product_{d|k} d^(k/d).

a(n) = Product_{k = 1..n} ((floor(n/k))!)^k.

a(n) = exp(Sum_{k = 1..n} log(k)/2 * floor(n/k) * floor(1 + n/k)). - Daniel Suteu, Sep 12 2018

log(a(n)) ~ c * n^2, where c = -zeta'(2)/2 = A073002/2 = 0.468774... - Vaclav Kotesovec, Jun 24 2021