This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A222056 #38 Nov 27 2024 16:41:49
%S A222056 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,
%T A222056 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,
%U A222056 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
%N A222056 Decimal expansion of (6/Pi^2)*Sum_{n>=1} 1/prime(n)^2.
%C A222056 This is the probability that the gcd of any two integers is prime. - _David Cushing_, Mar 27 2013
%C A222056 The asymptotic density of integers whose largest square divisor is a square of a prime (A082293). - _Amiram Eldar_, Jul 07 2020
%D A222056 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.2, p. 95.
%H A222056 Math StackExchange, <a href="http://math.stackexchange.com/questions/39665/given-2-randomly-chosen-integers-x-y-what-is-pk-gcdx-y">Given 2 randomly chosen integers x,y what is P(k=gcd(x,y))?</a>, May 2011.
%e A222056 0.27493346338652558891753873872267935690981646197586235178986...
%t A222056 Drop[Flatten[RealDigits[N[PrimeZetaP[2] 6/Pi^2, 100]]], -1] (* _Geoffrey Critzer_, Jan 17 2015 *)
%o A222056 (PARI) eps()=2.>>bitprecision(1.)
%o A222056 primezeta(s)=my(t=s*log(2)); sum(k=1,lambertw(t/eps())\t, moebius(k)/k*log(abs(zeta(k*s))))
%o A222056 primezeta(2)*6/Pi^2 \\ _Charles R Greathouse IV_, Jul 30 2016
%o A222056 (PARI) sumeulerrat(1/p, 2)/zeta(2) \\ _Amiram Eldar_, Mar 18 2021
%Y A222056 Cf. A059956, A082293, A085548.
%K A222056 nonn,cons,nice
%O A222056 0,1
%A A222056 _N. J. A. Sloane_, Feb 06 2013