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A131653 Decimal expansion of the sum of the reciprocals of squared 3-almost primes. 2
0, 3, 8, 5, 1, 6, 1, 9, 2, 9, 8, 2, 6, 9, 4, 6, 4, 0, 9, 1, 2, 8, 3, 7, 9, 2, 2, 6, 2, 8, 0, 6, 0, 3, 9, 5, 4, 3, 8, 9, 0, 0, 1, 6, 7, 4, 7, 8, 3, 8, 1, 5, 7, 1, 9, 3, 7, 1, 9, 1, 5, 5, 8, 9, 2, 2, 3, 7, 5, 5, 3, 7, 8, 3, 4, 5, 9, 1, 6, 6, 1, 3, 9, 3, 0, 4, 7, 4, 1, 4, 7, 6, 2, 0, 4, 9, 4, 7, 1, 5, 0, 8, 4, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
zeta(2) = A013661 is 1 plus a sum over inverse squares of k-almost primes, k=1 to infinity, where A085548 represents k=1, A117543 represents k=2 and this constant here represents k=3.
LINKS
R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009.
FORMULA
Equals A085548^3 / 6 + A085966 / 3 + A085548 * A085964 / 2.
Equals Sum_{i>=1} 1/A000290(A014612(i)).
EXAMPLE
0.038516192982694640912837922628060395438900167478381571937...
MATHEMATICA
RealDigits[PrimeZetaP[2]^3/6 + PrimeZetaP[6]/3 + PrimeZetaP[2]*PrimeZetaP[4]/2, 10, 120, -1][[1]] (* Amiram Eldar, Jun 25 2023 *)
CROSSREFS
Sequence in context: A016670 A021726 A221315 * A011239 A261644 A345449
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Sep 10 2007, Mar 07 2008
EXTENSIONS
a(104) corrected by Amiram Eldar, Jun 25 2023
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)