_R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Dec 04 2008

OEIS Server: https://oeis.org/edit/global/190

proposed

approved

R. J. Mathar, <a href="http://arxiv.org/abs/0803.0900">Series of reciprocal powers of k-almost primes</a>, constant B_{2,1} in table 8.

approved

proposed

The semiprime analog of A136141. To obtain the (smaller) sum over the square-freesquarefree semiprimes A006881, subtract the prime zeta functions of 4 ( A085964 ), 6, 8 etc . from this constant here. The first term in the representation as the geometric series in powers 1/q^s is in A117543 .

cons,nonn,new

equalsEquals 0.17105189297999663662220256437237421399124661203550059749107997... = 1/(4*3)+1/(6*5)+1/(9*8)+1/(10*9)+...

cons,nonn,new

Decimal expansion of the sum_q 1/(q*(q-1)) over the semiprimes q = A001358.

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

0,2

The semiprime analog of A136141. To obtain the (smaller) sum over the square-free semiprimes A006881, subtract the prime zeta functions of 4 ( A085964 ), 6, 8 etc from this constant here. The first term in the representation as the geometric series in powers 1/q^s is in A117543 .

equals 0.17105189297999663662220256437237421399124661203550059749107997... = 1/(4*3)+1/(6*5)+1/(9*8)+1/(10*9)+...

cons,nonn

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 04 2008

approved