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A119758 Numerator of Sum_{k=1..n} k^n/n^k. 1
1, 3, 20, 225, 3789, 89341, 2821552, 115377921, 5939637425, 375840753541, 28641787322796, 2583828842108449, 271949027324094925, 32986652806128680205, 4563200871898056653504, 713455071424061222336513 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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, Jun 27 2006
LINKS
FORMULA
a(n) = numerator(Sum_{k=1..n} k^n/n^k).
a(n) = n^(n-1)*(Sum_{k=1..n} k^n/n^k). - Alexander Adamchuk, 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, Jun 27 2006
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, Jun 27 2006 *)
PROG
(PARI) a(n) = numerator(prod(k=2, n, 1-1/(prime(k)-1)^2)); \\ Michel Marcus, May 31 2022
CROSSREFS
Cf. A000169.
Sequence in context: A052851 A262233 A058477 * A108527 A194972 A294603
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jun 18 2006, Jun 25 2006
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)