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%I #17 Jun 24 2021 16:28:35
%S 1,2,6,96,480,207360,1451520,2972712960,722369249280,5778953994240000,
%T 63568493936640000,9111096278347394580480000,
%U 118444251618516129546240000,10400352846118664303196241920000
%N a(n) = Product_{k = 1..n} A066841(k).
%C Conjecture: a(n) divides A092287(n) for all n - see comments in A129365.
%F a(n) = Product_{k = 1..n} Product_{d|k} d^(k/d).
%F a(n) = Product_{k = 1..n} ((floor(n/k))!)^k.
%F a(n) = exp(Sum_{k = 1..n} log(k)/2 * floor(n/k) * floor(1 + n/k)). - _Daniel Suteu_, Sep 12 2018
%F log(a(n)) ~ c * n^2, where c = -zeta'(2)/2 = A073002/2 = 0.468774... - _Vaclav Kotesovec_, Jun 24 2021
%t Table[Product[Floor[n/k]!^k, {k, 1, n}], {n, 1, 15}] (* _Vaclav Kotesovec_, Jun 24 2021 *)
%t Table[Product[k^(Floor[n/k]*(1 + Floor[n/k])/2), {k, 1, n}], {n, 1, 15}] (* _Vaclav Kotesovec_, Jun 24 2021 *)
%o (PARI) a(n) = prod(k=1, n, k^((n\k) * (1 + n\k) \ 2)); \\ _Daniel Suteu_, Sep 12 2018
%Y Cf. A007955, A066841, A092143, A092287, A129365.
%K nonn,easy
%O 1,2
%A _Peter Bala_, Apr 11 2007
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