A337768 Decimal expansion of the sum of reciprocals of squared composite numbers that are not prime powers.

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

Offset

0,2

Links

Table of n, a(n) for n=0..87.

Formula

Equals Sum_{k>=1} 1/(A024619(k)^2).

Equals zeta(2) - 1 - Sum_{k>1} P(2*k) = A013661 - 1 - A154945, where P is the prime zeta function. - Amiram Eldar, Sep 21 2020

Example

Equals 1/(6^2) + 1/(10^2) + 1/(12^2) + 1/(14^2) + ... + = 0.0932407691912272520326841426746816110874495234281701855...

Mathematica

A337768[n_] := 1/Select[Range[n, n], ! PrimePowerQ[#] && CompositeQ[#] &] N[Total[ParallelTable[A337768[k]^2, {k, 2, 10^8}]/.{} -> Sequence[]], 62]

Prog

(Sage)
sum_A337768 = (i for i in NN if i>3 and not i.is_prime() and not i.is_prime_power())
s = RLF(0); s
RealField(110)(s)
for i in range(0, 5000000): s += 1 / next(sum_A337768)^2
print(s) #

Crossrefs

Cf. A013661, A024619, A154945.

Sequence in context: A210113 A195704 A176516 * A372273 A210644 A072559

Adjacent sequences: A337765 A337766 A337767 * A337769 A337770 A337771

Keyword

nonn,cons

Author

Terry D. Grant, Sep 19 2020

Extensions

More terms from Amiram Eldar, Sep 21 2020

Status

approved