

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.


1



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
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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 * A244854 A144807 A157957
Adjacent sequences: A247665 A247666 A247667 * A247669 A247670 A247671


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, Sep 22 2014


STATUS

approved



