login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Decimal expansion of Product_{q in A001358} (1-1/(q*(q-1))).
1

%I #3 Mar 30 2012 17:39:45

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

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

%N Decimal expansion of Product_{q in A001358} (1-1/(q*(q-1))).

%C Semiprime analog of A005596.

%H R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products over all positive integers</a>, arXiv:0903.2514 [math.NT], Table 3 third line. [From _R. J. Mathar_, Mar 28 2009]

%F The logarithm is -sum_{s>=2} sum_{j=1..floor[s/(1+r)]} binomial(s-r*j-1,j-1)*P_2(s)/j at r=1, where P_k(s) are the k-almost prime zeta functions of arXiv:0803.0900.

%e 0.839042154274468600768... = (1-1/12)*(1-1/30)*(1-1/72)*(1-1/90)*(1-1/182)*..

%K nonn,cons,less

%O 0,1

%A _R. J. Mathar_, Feb 13 2009