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A247605 Decimal expansion of the coefficient c_md in c_md*log(N)^(1/rho), the asymptotic mean number of distinct factors in a random factorization of n <= N. 0
1, 4, 8, 7, 9, 1, 5, 9, 7, 1, 6, 7, 8, 1, 5, 7, 8, 9, 2, 8, 7, 1, 6, 8, 6, 3, 0, 5, 4, 6, 5, 5, 6, 6, 0, 7, 2, 7, 9, 1, 9, 8, 8, 4, 9, 0, 4, 5, 2, 7, 1, 7, 9, 1, 8, 9, 7, 1, 1, 1, 7, 9, 7, 4, 5, 3, 8, 5, 7, 8, 5, 4, 4, 4, 6, 2, 5, 3, 5, 4, 3, 5, 6, 8, 6, 5, 8, 9, 2, 4, 8, 7, 1, 6, 6, 3, 7, 1, 2, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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=1..101.

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

FORMULA

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

EXAMPLE

1.48791597167815789287168630546556607279198849...

MATHEMATICA

digits = 101; rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> digits + 5]; cmd = (-1/rho)*Gamma[-1/rho]*(-1/Zeta'[rho])^(1/rho); RealDigits[cmd, 10, digits] // First

CROSSREFS

Cf. A107311, A217598, A247667.

Sequence in context: A337606 A019924 A021209 * A244000 A201937 A211456

Adjacent sequences:  A247602 A247603 A247604 * A247606 A247607 A247608

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Sep 22 2014

STATUS

approved

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Last modified September 25 16:17 EDT 2021. Contains 347658 sequences. (Running on oeis4.)