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

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
scdc[n_] := 1/(Select[Range[n, n], CompositeQ[#] && ! perfPQ[#] &])
N[Total[ParallelTable[scdc[k]^2, {k, 2, 10^8}] /. {} -> Sequence[]], 100]

Prog

(Sage)
sum_A335086 = (i for i in NN if i>3 and not i.is_prime() and not i.is_perfect_power())
s = RLF(0); s
RealField(110)(s)
for i in range(0, 5000000): s += 1 / next(sum_A335086)^2
print(s) #

Crossrefs

Cf. A106543.

Cf. A013661, A085548.

Sequence in context: A239908 A293171 A334689 * A151898 A080994 A340809

Adjacent sequences: A335083 A335084 A335085 * A335087 A335088 A335089

Keyword

nonn,cons

Author

Terry D. Grant, Sep 11 2020

Extensions

a(7)-a(16) from Jinyuan Wang, Nov 07 2020

More digits from Jon E. Schoenfield, Jan 26 2021

Status

approved