A335086 - OEIS

A335086

Decimal expansion of the sum of reciprocals of squared composite numbers that are not perfect powers.

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

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OFFSET

-1,1

LINKS

Table of n, a(n) for n=-1..103.

FORMULA

Equals Sum_{k>=1} 1/(A106543(k)^2).

Equals zeta(2) - P(2) - 1 - Sum_{k>=2} mu(k)*(1-zeta(2*k)), where P(s) is the prime zeta function. - Amiram Eldar, Dec 03 2022

EXAMPLE

Equals 1/(6^2) + 1/(10^2) + 1/(12^2) + 1/(14^2) + ... = 0.092211319607067162105722850170097751152689718042181...

MATHEMATICA

perfPQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1