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Search: id:A119682
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| A119682 |
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Numerator of Sum (-1)^(k+1)*1/k^2, k = 1..n. |
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+0
21
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| 1, 3, 31, 115, 3019, 973, 48877, 191833, 5257891, 5194387, 634871227, 629535127, 107159834863, 106497287263, 107074439839, 426268707331, 123711093737059, 41082589491553, 14880853934789833, 2967138724292741, 2975331071381381
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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p divides a(p-1) for prime p > 2 - similar to Wolstenholme's theorem for A007406(n) ( numerator of Sum 1/k^2, k = 1..n ).
Also a(n) = Sqrt[Numerator[Sum[Sum[(-1)^(i+j)*1/(i*j)^2, {i, 1, n}], {j, 1, n}]]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 26 2006
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FORMULA
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a(n) = numerator[ Sum[ (-1)^(k+1)*1/k^2, {k,1, n} ] ].
Also a(n) = Abs[Numerator[Sum[Sum[(-1)^(i+j) * j/i^2, {i, 1, n}], {j, 1, n}]]]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 26 2006
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MATHEMATICA
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Sqrt[Numerator[Table[Sum[Sum[(-1)^(i+j)*1/(i*j)^2, {i, 1, n}], {j, 1, n}], {n, 1, 20}]]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 26 2006
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PROGRAM
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(PARI) Numerator[Table[Sum[(-1)^(i+1)*1/i^2, {i, 1, n}], {n, 1, 40}]]
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CROSSREFS
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Cf. A007406.
Sequence in context: A104312 A107197 A096060 this_sequence A069630 A069615 A087389
Adjacent sequences: A119679 A119680 A119681 this_sequence A119683 A119684 A119685
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 08 2006, Jun 25 2006
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