OFFSET
0,1
COMMENTS
This is the probability that the gcd of any two integers is prime. - David Cushing, Mar 27 2013
The asymptotic density of integers whose largest square divisor is a square of a prime (A082293). - Amiram Eldar, Jul 07 2020
LINKS
Math StackExchange, Given 2 randomly chosen integers x,y what is P(k=gcd(x,y))?, May 2011.
EXAMPLE
0.27493346338652558891753873872267935690981646197586235178986...
MATHEMATICA
Drop[Flatten[RealDigits[N[PrimeZetaP[2] 6/Pi^2, 100]]], -1] (* Geoffrey Critzer, Jan 17 2015 *)
PROG
(PARI) eps()=2.>>bitprecision(1.)
primezeta(s)=my(t=s*log(2)); sum(k=1, lambertw(t/eps())\t, moebius(k)/k*log(abs(zeta(k*s))))
primezeta(2)*6/Pi^2 \\ Charles R Greathouse IV, Jul 30 2016
(PARI) sumeulerrat(1/p, 2)/zeta(2) \\ Amiram Eldar, Mar 18 2021
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Feb 06 2013
STATUS
approved