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

0,1

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

References

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

Links

Table of n, a(n) for n=0..101.

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

Cf. A059956, A082293, A085548.

Sequence in context: A011050 A198935 A019779 * A247448 A329064 A102514

Adjacent sequences: A222053 A222054 A222055 * A222057 A222058 A222059

Keyword

nonn,cons,nice

Author

N. J. A. Sloane, Feb 06 2013

Status

approved