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
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
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jun 18 2006, Jun 25 2006
STATUS
approved