A346011 Decimal expansion of Sum_{p prime} (1 - 1/(2*p) + (p - 1)*log(1 - 1/p)).

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, 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, 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

Offset

-1,1

Comments

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

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

Links

Table of n, a(n) for n=-1..98.

R. L. Duncan, Note on the divisors of a number, The American Mathematical Monthly, Vol. 68, No. 4 (1961), pp. 356-359.

Sébastien Gaboury, Sur les convolutions de fonctions arithmétiques, M.Sc. thesis, Laval University, Quebec, 2007.

Formula

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

Example

0.09562819731410333141161338161335164509163393150425...

Mathematica

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

Crossrefs

Cf. A346009, A346010, A346012, A346013.

Sequence in context: A262276 A244844 A255896 * A019882 A366545 A292824

Adjacent sequences: A346008 A346009 A346010 * A346012 A346013 A346014

Keyword

nonn,cons

Author

Amiram Eldar, Jul 01 2021

Status

approved