A222056 Decimal expansion of (6/Pi^2)*Sum_{n>=1} 1/prime(n)^2.

2, 7, 4, 9, 3, 3, 4, 6, 3, 3, 8, 6, 5, 2, 5, 5, 8, 8, 9, 1, 7, 5, 3, 8, 7, 3, 8, 7, 2, 2, 6, 7, 9, 3, 5, 6, 9, 0, 9, 8, 1, 6, 4, 6, 1, 9, 7, 5, 8, 6, 2, 3, 5, 1, 7, 8, 9, 8, 6, 0, 3, 4, 4, 7, 3, 6, 2, 4, 1, 6, 3, 1, 7, 2, 0, 3, 1, 7, 5, 7, 6, 9, 4, 1, 5, 6, 1, 2, 7, 3, 8, 3, 2, 1, 8, 7, 1, 2, 2, 4, 9, 0

Offset: 0

Author

N. J. A. Sloane, Feb 06 2013

Keywords

• nonn
• cons
• nice

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

Examples

			0.27493346338652558891753873872267935690981646197586235178986...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.2, p. 95.

Links

• Math StackExchange, Given 2 randomly chosen integers x,y what is P(k=gcd(x,y))?, May 2011.

Crossrefs

Cf. A059956, A082293, A085548.

Programs

Mathematica

Drop[Flatten[RealDigits[N[PrimeZetaP[2] 6/Pi^2, 100]]], -1] (* Geoffrey Critzer, Jan 17 2015 *)

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