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
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.
Programs
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Mathematica
RealDigits[Zeta'[2] - (Pi^2/6)*EulerGamma, 10, 105] // First
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PARI
default(realprecision, 100); zeta'(2) - zeta(2)*Euler \\ G. C. Greubel, Sep 06 2018
Formula
B = -integral_{y>0} log(1-e^(-y))*log(y) dy = zeta'(2) - (Pi^2/6)*gamma.