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A129364
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a(n) = Product_{k = 1..n} A066841(k).
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3
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1, 2, 6, 96, 480, 207360, 1451520, 2972712960, 722369249280, 5778953994240000, 63568493936640000, 9111096278347394580480000, 118444251618516129546240000, 10400352846118664303196241920000
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) divides A092287(n) for all n - see comments in A129365.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = prod(k=1, n, k^((n\k) * (1 + n\k) \ 2)); \\ Daniel Suteu, Sep 12 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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