login
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
OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2024, 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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved