A068589 -id:A068589

Search: a068589 -id:a068589

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A334580

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

+0
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

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.

MAPLE

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

seq(denom(b(n)), n=1..30);

PROG

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

CROSSREFS

Cf. A068589, A119682 (numerators).

KEYWORD

nonn,frac

AUTHOR

Petros Hadjicostas, May 06 2020

STATUS

approved

A069117

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

+0
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

PROG

(PARI) 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, ", ")))

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Apr 07 2002

STATUS

approved

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