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A335086
Decimal expansion of the sum of reciprocals of squared composite numbers that are not perfect powers.
1
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
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.
Sequence in context: A239908 A293171 A334689 * A151898 A080994 A340809
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