A131653 - OEIS

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A131653

Decimal expansion of the sum of the reciprocals of squared 3-almost primes.

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

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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

Table of n, a(n) for n=0..104.

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

Cf. A000290, A013661, A014612, A085548, A085964, A085966, A117543, A085548.