OFFSET
0,2
COMMENTS
Consider the constants N(s) = Sum_{n>=2} 1/(n^s*(n-1)) = s-Sum_{k=2..s} zeta(k), where zeta() is Riemann's zeta function. We have N(1)=1 and this constant here is N(3).
LINKS
R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009, section 4.1.
EXAMPLE
0.15300902999217927812784667184252482001606380645270268047217021528815...
MAPLE
evalf(3-Pi^2/6-Zeta(3));
MATHEMATICA
RealDigits[3-Pi^2/6-Zeta[3], 10, 120][[1]] (* Harvey P. Dale, Jul 01 2022 *)
PROG
(PARI) 3-Pi^2/6-zeta(3) \\ Charles R Greathouse IV, Jan 31 2017
(Sage) t(n) = 1/(n*(n+1)^(3));
sum(t(n), n, 1, oo).n(digits=107); # Jani Melik, Nov 20 2020
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Dec 03 2008
STATUS
approved