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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
OFFSET
0,2
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
KEYWORD
nonn,cons
AUTHOR
Terry D. Grant, Sep 19 2020
EXTENSIONS
More terms from Amiram Eldar, Sep 21 2020
STATUS
approved