A346011 - OEIS

A346011

Decimal expansion of Sum_{p prime} (1 - 1/(2*p) + (p - 1)*log(1 - 1/p)).

%I #4 Jul 01 2021 16:12:22

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

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

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

%N Decimal expansion of Sum_{p prime} (1 - 1/(2*p) + (p - 1)*log(1 - 1/p)).

%C This constant appears in the asymptotic formula for A346009(n)/A346010(n), the average number of distinct prime factors of the divisors of n.

%C The asymptotic mean of A346012(n)/A346013(n).

%H R. L. Duncan, <a href="https://www.jstor.org/stable/2311587">Note on the divisors of a number</a>, The American Mathematical Monthly, Vol. 68, No. 4 (1961), pp. 356-359.

%H Sébastien Gaboury, <a href="http://hdl.handle.net/20.500.11794/18899">Sur les convolutions de fonctions arithmétiques</a>, M.Sc. thesis, Laval University, Quebec, 2007.

%F Equals Sum_{k>=2} P(k)/(k*(k+1)), where P(s) is the prime zeta function.

%e 0.09562819731410333141161338161335164509163393150425...

%t $MaxExtraPrecision = 500; m = 500; RealDigits[NSum[(PrimeZetaP[n])/(n*(n + 1)), {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m], 10, 100][[1]]

%Y Cf. A346009, A346010, A346012, A346013.

%K nonn,cons

%O -1,1

%A _Amiram Eldar_, Jul 01 2021