A068589 -id:A068589 - cp's OEIS frontend

A069117 Numbers n such that A068589(n) is a perfect square.

1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 27, 28, 29, 30, 31, 32, 63, 64, 65, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 105, 106, 107, 108, 109, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 189, 190, 191, 192, 193, 194, 195

Offset: 1

Benoit Cloitre, Apr 07 2002

precision 1000 digits : for(n=1,300,if(sqrt(denominator(sum(i=1,n,1/i^3))/denominator(sum(i=1,n,1/i))) == floor(sqrt(denominator(sum(i=1,n,1/i^3))/denominator(sum(i=1,n,1/i)))),print1(n,",")))

A334580 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.

Original entry on oeis.org

1, 4, 36, 144, 3600, 1200, 58800, 235200, 6350400, 6350400, 768398400, 768398400, 129859329600, 129859329600, 129859329600, 519437318400, 150117385017600, 50039128339200, 18064125330451200, 3612825066090240, 3612825066090240, 3612825066090240, 1911184459961736960

Offset: 1

Petros Hadjicostas, May 06 2020

For n = 1 to n = 19, we have a(n) = A068589(n), but a(20) = 3612825066090240 <> A068589(20) = 18064125330451200.

			The first few fractions are 1, 3/4, 31/36, 115/144, 3019/3600, 973/1200, 48877/58800, 191833/235200, 5257891/6350400, 5194387/6350400, ... = A119682/A334580.

Cf. A068589, A119682 (numerators).

b := proc(n) local k: add((-1)^(k + 1)/k^2, k = 1 .. n): end proc:
seq(denom(b(n)), n=1..30);

a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^2)); \\ Michel Marcus, May 07 2020

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A069117 Numbers n such that A068589(n) is a perfect square.

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A334580 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.

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