A247668 Decimal expansion of the coefficient c_v in c_v*log(N), the asymptotic variance of the number of factors in a random factorization of n <= N.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.

Links

Table of n, a(n) for n=0..101.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 37.

Formula

c_v = (-1/zeta'(rho))*(zeta''(rho)/zeta'(rho]^2 - 1), where rho = 1.728647... is A107311, the real solution to zeta(rho) = 2.

Example

0.308403444608077001633607726174587986672094960536886...

Mathematica

digits = 102; rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> digits+5]; cv = (-1/Zeta'[rho])*(Zeta''[rho]/Zeta'[rho]^2 - 1); RealDigits[cv, 10, digits] // First

Crossrefs

Cf. A107311, A217598, A247667.

Sequence in context: A174474 A317300 A007391 * A359258 A244854 A144807

Adjacent sequences: A247665 A247666 A247667 * A247669 A247670 A247671

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 22 2014

Status

approved