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

0,2

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.

Links

Table of n, a(n) for n=0..101.

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.

Example

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

Mathematica

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

Crossrefs

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

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

Sequence in context: A272876 A133930 A077892 * A242970 A070433 A169821

Adjacent sequences: A117540 A117541 A117542 * A117544 A117545 A117546

Keyword

cons,nonn

Author

T. D. Noe, Mar 28 2006

Status

approved