A127901 Denominators of convergents to 6/Pi^2 based on 1/Zeta(s) = Sum_{k>=1} (mu(k)/k^s).

1, 4, 36, 900, 75, 3675, 14700, 1778700, 300600300, 150300150, 450900450, 130310230050, 47041993048050, 47041993048050, 94083986096100, 49770428644836900, 12442607161209225, 10464232622576958225, 41856930490307832900, 40224510201185827416900

Offset

1,2

References

John Derbyshire, "Prime Obsession", Joseph Henry Press, 2003, p. 249.

Links

Table of n, a(n) for n=1..20.

Formula

Partial sums of convergents to 6/Pi^2 = 1/Zeta(2) = Sum_{k>=1} (mu(k)/k^2) = 1 - 1/2^2 - 1/3^2 - 1/5^2 + 1/6^2 ...

Example

First few convergents to 6/Pi^2 are: 1/1, 3/4, 23/36, 539/900, 47/75, 2228/3675, 9059/14700, ...

Mathematica

Denominator @ Accumulate[DeleteCases[Table[MoebiusMu[k]/k^2, {k, 1, 40}], 0]] (* Amiram Eldar, Feb 26 2020 *)

Crossrefs

Cf. A013661, A055615 (n*mu(n)), A059956, A127900 (numerators of convergents).

Sequence in context: A353996 A009446 A134052 * A061742 A136469 A120605

Adjacent sequences: A127898 A127899 A127900 * A127902 A127903 A127904

Keyword

nonn,frac

Author

Gary W. Adamson, Feb 04 2007

Extensions

More terms from Amiram Eldar, Feb 26 2020

Status

approved