A242051 Decimal expansion of B, a constant appearing in the asymptotic number of integers the prime factorization of which has decreasing exponents.

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

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 9.

L. B. Richmond, Asymptotic results for partitions (I) and the distribution of certain integers, Journal of Number Theory 8, 372-389 (1976) p. 388.

Formula

B = -integral_{y>0} log(1-e^(-y))*log(y) dy = zeta'(2) - (Pi^2/6)*gamma.

Mathematica

RealDigits[Zeta'[2] - (Pi^2/6)*EulerGamma, 10, 105] // First

Prog

(PARI) default(realprecision, 100); zeta'(2) - zeta(2)*Euler \\ G. C. Greubel, Sep 06 2018

Crossrefs

Cf. A001620, A073002.

Sequence in context: A277235 A241058 A248570 * A263030 A217171 A357145

Adjacent sequences: A242048 A242049 A242050 * A242052 A242053 A242054

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 13 2014

Status

approved