A091589 Decimal expansion of the analog of the Mertens constant B_2 in the asymptotic series for the variance of the number of prime factors Omega.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 95.

Links

Table of n, a(n) for n=0..99.

Terence Tao and Joni Teräväinen, Quantitative correlations and some problems on prime factors of consecutive integers, arXiv:2512.01739 [math.NT], 2025. See p. 2.

Eric Weisstein's World of Mathematics, Prime Factor.

Formula

Equals A083342 minus Pi^2/6 plus A086242. - R. J. Mathar, Oct 14 2010

Equals lim_{m->oo} ((1/m) * Sum_{k=1..m} A001222(k)^2 - ((1/m) * Sum_{k=1..m} A001222(k))^2 - log(log(m))). - Amiram Eldar, Jan 09 2024

Example

0.764784809797846763064632262341...

Crossrefs

Cf. A001222, A013661 (Pi^2/6), A086242, A083342.

Sequence in context: A021089 A154194 A389024 * A100322 A341328 A094961

Adjacent sequences: A091586 A091587 A091588 * A091590 A091591 A091592

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 22 2004

Extensions

More digits from R. J. Mathar, Oct 14 2010

More digits (using terms in A083342 and A086242) from Vaclav Kotesovec, Aug 12 2019

Status

approved