OFFSET
0,3
COMMENTS
Density of the fourth-root-smooth numbers.
REFERENCES
Karl Dickman, On the frequency of numbers containing prime factors of a certain relative magnitude, Arkiv för Matematik, Astronomi och Fysik 22A 10 (1930), pp. 1-14.
LINKS
David Broadhurst, Dickman polylogarithms and their constants arXiv:1004.0519 [math-ph], 2010.
EXAMPLE
F(1/4) = 0.00491092564776083235273915092361518603248429741769294597796...
MATHEMATICA
RealDigits[1-Log[4]+PolyLog[2, 1/4]+2*Log[2]^2-Pi^2/12-PolyLog[3, 1/4]-PolyLog[2, 1/4]*Log[2]-2/3*Log[2]^3+13*Zeta[3]/24, 10, 100, -1][[1]] (* Vaclav Kotesovec, Jul 15 2014 *)
PROG
(PARI) 1-log(4)+polylog(2, 1/4)+2*log(2)^2-Pi^2/12-polylog(3, 1/4)-polylog(2, 1/4)*log(2)-2/3*log(2)^3+13*zeta(3)/24
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Charles R Greathouse IV, Jul 14 2014
STATUS
approved