A119756 - OEIS

A119756

Numerator of n/1^n + (n-1)/2^n + (n-2)/3^n + ... + 2/(n-1)^n + 1/n^n.

%I #3 Mar 31 2012 13:20:27

%S 1,9,355,87425,666094597,283878143843,1354313329376085811,

%T 24568316785788956621809,3695039511560825652073500196447,

%U 20673934657221575836904008710237871

%N Numerator of n/1^n + (n-1)/2^n + (n-2)/3^n + ... + 2/(n-1)^n + 1/n^n.

%C a(p-1) is divisible by p^2 for prime p>2. a(p-2) is divisible by p for prime p>3. a(n) = (n+1)*(Zeta[n] - Zeta[n,n+1]) - Zeta[n-1] + Zeta[n-1,n+1].

%F a(n) = numerator[ Sum[ (n+1-i)/i^n, {i,1,n} ]].

%t Table[Numerator[Sum[(n+1-i)/i^n,{i,1,n}]],{n,1,13}]

%K frac,nonn

%O 1,2

%A _Alexander Adamchuk_, Jun 17 2006