A127900 Numerators in convergents to 6/Pi^2 using 1/Zeta(s) = Sum_{k>=1} (mu(k)/k^s).

1, 3, 23, 539, 47, 2228, 9059, 1081439, 180984491, 91259083, 275781251, 79249881089, 28478896843079, 28585568029129, 57365524459283, 30252278452864607, 7581475836827408, 6363578571610640903, 25407806585897777131, 24375045198557455989991

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 1/Zeta(s) = Sum_{k>=1} (mu(k)/k^s) with s = 2; 1/Zeta(2) = 6/Pi^2.

Example

1/Zeta(2) = 6/Pi^2 = 1 - 1/2^2 - 1/3^2 - 1/5^2 + 1/6^2 - 1/7^2 + 1/10^2 ...
with convergents: 1/1, 3/4, 23/36, 539/900, 47/75, 2228/3675, 9059/14700, ...

Mathematica

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

Crossrefs

Cf. A013661, A055615 (n*mu(n)), A059956, A127901 (denominators of convergents).

Sequence in context: A154896 A134050 A101191 * A229266 A143985 A333739

Adjacent sequences: A127897 A127898 A127899 * A127901 A127902 A127903

Keyword

nonn,frac

Author

Gary W. Adamson, Feb 04 2007

Extensions

More terms from Amiram Eldar, Feb 26 2020

Status

approved