A119784 Numerator of Sum[Sum[(-1)^(i+1)*1/(i*j)^2, {i, 1, n}], {j, 1, n}].

1, 15, 1519, 23575, 15907111, 5224037, 13034567237, 206747823917, 51412399560631, 10224262569323, 152012226379719803, 151406414338463843, 4372018721271579430163, 4359099317599237566323, 21975413631947472215359

Offset: 1

Author

Alexander Adamchuk, Jun 25 2006

Keywords

• frac
• nonn

Comments

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

Crossrefs

Cf. A007406, A119682.

Programs

Mathematica

Numerator[Table[Sum[Sum[(-1)^(i+1)*1/(i*j)^2, {i, 1, n}], {j, 1, n}],{n,1,20}]]

Formula

a(n) = numerator[Sum[Sum[(-1)^(i+1)*1/(i*j)^2, {i, 1, n}], {j, 1, n}]]. a(n) = A119682(n)*A007406(n).