A120286 - OEIS

%I #9 May 02 2024 10:46:42

%S 1,9,65,725,3899,28763,419017,864669,7981633,3586319,200763407,

%T 2649665993,34899471137,176508049513,356606957297,12234391348253,

%U 209672027529221,4012917216669239,15350275129353301,15443118015171841

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

%C p^2 divides a(p-1) for prime p>2. p divides a(p-2) for prime p>3.

%F a(n) = numerator[Sum[Sum[1/i^2,{i,1,k}],{k,1,n}]].

%t Numerator[Table[Sum[Sum[1/i^2,{i,1,k}],{k,1,n}],{n,1,30}]]

%t Table[-EulerGamma + HarmonicNumber[1 + n, 2] + n*HarmonicNumber[1 + n, 2] - PolyGamma[0, 2 + n], {n, 1, 20}] // Numerator (* _Vaclav Kotesovec_, May 02 2024 *)

%o (Python)

%o from fractions import Fraction

%o def A120286(n): return sum(Fraction(n-i+1,i**2) for i in range(1,n+1)).numerator # _Chai Wah Wu_, May 01 2024

%Y Cf. A027612, A001008, A007406, A007407, A370774 (denom.).

%K frac,nonn

%O 1,2

%A _Alexander Adamchuk_, Jul 07 2006