A335086 -id:A335086

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A335590

Decimal expansion of the sum of the reciprocals of the squares of the perfect powers > 1.

+10
0

1, 0, 0, 4, 7, 5, 3, 2, 7, 2, 0, 0, 0, 9, 3, 7, 7, 5, 8, 6, 0, 1, 4, 8, 9, 5, 1, 6, 4, 3, 6, 7, 9, 5, 0, 3, 8, 9, 3, 0, 2, 8, 8, 3, 9, 9, 2, 4, 7, 2, 4, 4, 8, 9, 4, 5, 6, 1, 9, 2, 9, 4, 0, 6, 1, 0, 6, 3, 5, 7, 7, 3, 4, 9, 4, 4, 6, 9, 2, 1, 7, 0, 5, 0, 9, 5, 8, 5, 2, 0, 5, 1, 2, 1, 8, 1, 6, 3, 9, 7, 6, 2, 0, 5, 7

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

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Equals Sum_{k>=2} 1/A001597(k)^2.

Equals Sum_{k>=2} mu(k)*(1 - zeta(2*k)). - Amiram Eldar, Jan 27 2021

EXAMPLE

Equals 1/4^2 + 1/8^2 + 1/9^2 + 1/16^2 + 1/25^2 + 1/27^2 + 1/32^2 + 1/36^2 + 1/49^2 + 1/64^2 + 1/81^2 + 1/100^2 + ... = 0.10047532720009377586014895164367950389302883992472...

MATHEMATICA

RealDigits[Sum[MoebiusMu[k]*(1 - Zeta[2*k]), {k, 2, 200}], 10, 105][[1]] (* Amiram Eldar, Jan 27 2021 *)

PROG

(PARI) suminf(k=2, moebius(k)*(1-zeta(2*k))) \\ Hugo Pfoertner, Jan 27 2021

CROSSREFS

Cf. A001597, A013661, A085548, A275647, A335086, A335589, A340588.

KEYWORD

nonn,cons

AUTHOR

Jon E. Schoenfield, Jan 26 2021

STATUS

approved

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