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A119758
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Numerator of Sum_{k=1..n} k^n/n^k.
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1
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1, 3, 20, 225, 3789, 89341, 2821552, 115377921, 5939637425, 375840753541, 28641787322796, 2583828842108449, 271949027324094925, 32986652806128680205, 4563200871898056653504, 713455071424061222336513
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OFFSET
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1,2
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COMMENTS
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a(p-1) is divisible by prime p>2. a(p) is divisible by ((p+1)/2)^2 for prime p>2.
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LINKS
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FORMULA
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a(n) = numerator(Sum_{k=1..n} k^n/n^k).
a(2m) is divisible by 2m+1 for integer m>0. a(2m-1) is divisible by m^2 for integer m>0. - Alexander Adamchuk, Jun 27 2006
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MATHEMATICA
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Table[Numerator[Sum[k^n/n^k, {k, 1, n}]], {n, 1, 20}]
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PROG
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(PARI) a(n) = numerator(prod(k=2, n, 1-1/(prime(k)-1)^2)); \\ Michel Marcus, May 31 2022
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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