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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 Table of n, a(n) for n=1..16. 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. A023037, A031971. Cf. A000169. Sequence in context: A052851 A262233 A058477 * A108527 A194972 A294603 Adjacent sequences: A119755 A119756 A119757 * A119759 A119760 A119761 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.)