A117543 Decimal expansion of the sum of the reciprocals of squared semiprimes.

1, 4, 0, 7, 6, 0, 4, 3, 4, 3, 4, 9, 0, 2, 3, 3, 8, 8, 2, 2, 2, 7, 5, 0, 9, 2, 5, 4, 1, 3, 8, 7, 7, 2, 5, 3, 7, 7, 4, 9, 1, 9, 2, 7, 6, 0, 0, 4, 8, 8, 0, 2, 6, 3, 9, 2, 4, 1, 4, 8, 9, 7, 6, 8, 0, 7, 8, 9, 3, 8, 0, 2, 8, 0, 9, 7, 6, 0, 3, 5, 3, 8, 6, 9, 6, 3, 5, 0, 4, 4, 3, 4, 8, 6, 1, 3, 1, 3, 8, 2, 5, 7

Offset: 0

Author

T. D. Noe, Mar 28 2006

Keywords

• cons
• nonn

Comments

Geoffrey Landis and Jonathan Vos Post (personal communication) show that this constant equals ((P2)^2 + P4)/2, where P2 and P4 are constants in A085548 and A085964, respectively.

Examples

			0.14076043434902338822275... = 1/4^2 + 1/6^2 + 1/9^2 + 1/10^2 + 1/14^2 +1/15^2 +...
		

Links

• Richard J. Mathar, Series of Reciprocal Powers of k-almost Primes, arXiv:0803.0900 [math.NT], 2008-2009. See Table 4.
• Eric Weisstein's World of Mathematics, Prime Zeta Function.

Crossrefs

Cf. A001358 (semiprimes), A154928 (derivative).

Cf. A131653 (squared triprimes). [T. D. Noe, Oct 09 2008]

Programs

Mathematica

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