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A337768 Decimal expansion of the sum of reciprocals of squared composite numbers that are not prime powers. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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 * A210644 A072559 A019941

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

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Last modified June 20 04:43 EDT 2021. Contains 345157 sequences. (Running on oeis4.)