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A127901 Denominators of convergents to 6/Pi^2 based on 1/Zeta(s) = Sum_{k>=1} (mu(k)/k^s). 1
1, 4, 36, 900, 75, 3675, 14700, 1778700, 300600300, 150300150, 450900450, 130310230050, 47041993048050, 47041993048050, 94083986096100, 49770428644836900, 12442607161209225, 10464232622576958225, 41856930490307832900, 40224510201185827416900 (list; graph; refs; listen; history; text; internal format)
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: A126152 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

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Last modified September 20 21:32 EDT 2021. Contains 347591 sequences. (Running on oeis4.)