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

Offset: 0

Author

R. J. Mathar, Sep 10 2007, Mar 07 2008

Keywords

• cons
• nonn

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.

Examples

			0.038516192982694640912837922628060395438900167478381571937...
		

Links

• R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009.

Crossrefs

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

Programs

Mathematica

RealDigits[PrimeZetaP[2]^3/6 + PrimeZetaP[6]/3 + PrimeZetaP[2]*PrimeZetaP[4]/2, 10, 120, -1][[1]] (* Amiram Eldar, Jun 25 2023 *)

Formula

Equals A085548^3 / 6 + A085966 / 3 + A085548 * A085964 / 2.

Equals Sum_{i>=1} 1/A000290(A014612(i)).

Extensions

a(104) corrected by Amiram Eldar, Jun 25 2023