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A248695
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Decimal expansion of sum_{n >= 1} n!/p(n), where p(n) = [n/1]!*[n/2]!*...*[n/n]!, and [ ] = floor.
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2
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2, 9, 2, 4, 9, 9, 2, 7, 8, 7, 4, 3, 1, 2, 8, 5, 5, 1, 4, 5, 0, 0, 1, 5, 6, 0, 9, 4, 1, 7, 4, 4, 2, 4, 0, 1, 3, 2, 8, 9, 9, 8, 3, 9, 3, 1, 0, 2, 2, 9, 3, 1, 2, 1, 8, 0, 5, 0, 9, 4, 1, 3, 2, 9, 6, 8, 6, 9, 2, 5, 8, 8, 3, 7, 3, 3, 9, 2, 4, 9, 3, 5, 3, 5, 4, 7
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OFFSET
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6,1
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COMMENTS
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Let t(n) = n!/p(n). Then t(n) is an integer for n = 1..15, and max{t(n), n = 1..infinity}} = t(23) = 77452.802... . It appears that t(n) < 1/10 for n > 35 and t(n) < 10^(-6) for n > 45.
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LINKS
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EXAMPLE
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292499.27874312855145001560941744240132899839310229312180509413296869258837339...
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MAPLE
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evalf(sum(n!/product(floor(n/k)!, k=2..n), n=1..infinity), 120); # Vaclav Kotesovec, Oct 19 2014
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MATHEMATICA
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u = N[Sum[n!/Product[Floor[n/k]!, {k, 2, n}], {n, 1, 200}], 130]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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