A119785 - OEIS

%I #2 Mar 31 2012 13:20:27

%S 1,25,343,1025,57959,488579,266681,18321733,185784679,21651619,

%T 5507071447,15632832085,40799043101,1187015026009,6362282386111,

%U 13990468150733,238357395880861,167890966963712483,86364397717734821

%N Numerator of the product of the n-th square pyramidal number and the n-th generalized harmonic number in power 2.

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

%F a(n) = numerator[Sum[i^2,{i,1,n}] * Sum[1/j^2,{j,1,n}]] = numerator[n(n+1)(2n+1)/6 * Sum[1/j^2,{j,1,n}]] = numerator[A000330(n) * ( A007406(n)/A007407(n) )]. Also a(n) = numerator[Sum[Sum[i^2/j^2, {i, 1, n}], {j, 1, n}]].

%t Numerator[Table[n(n+1)(2n+1)/6*Sum[1/k^2,{k,1,n}],{n,1,30}]]. Numerator[Table[Sum[Sum[i^2/j^2, {i, 1, n}], {j, 1, n}],{n,1,30}]].

%Y Cf. A000330, A007406, A007407.

%K frac,nonn

%O 1,2

%A _Alexander Adamchuk_, Jun 25 2006