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A119758
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Numerator of Sum [ k^n/n^k, {k,1,n} ].
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(p-1) is divisible by prime p>2. a(p) is divisible by ((p+1)/2)^2 for prime p>2.
Denominator of Sum[k^n/n^k,{k,1,n}] is equal to n^(n-1) = A000169(n). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 27 2006
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FORMULA
| a(n) = numerator[ Sum [ k^n/n^k, {k,1,n} ]].
a(n) = Sum[k^n/n^k,{k,1,n}]*n^(n-1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 27 2006
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 (alex(AT)kolmogorov.com), Jun 27 2006
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MATHEMATICA
| Table[Numerator[Sum[k^n/n^k, {k, 1, n}]], {n, 1, 20}]
Table[Sum[k^n/n^k, {k, 1, n}]*n^(n-1), {n, 1, 50}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 27 2006
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CROSSREFS
| Cf. A023037, A031971.
Cf. A000169.
Sequence in context: A206405 A052851 A058477 * A108527 A194972 A195135
Adjacent sequences: A119755 A119756 A119757 * A119759 A119760 A119761
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 18 2006, Jun 25 2006
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