There's also the paper arxiv:1612.03700 "The probability that two random integers are coprime" which relates the best remainder to the RH. On Wed, Jul 15, 2020 at 12:00 PM Neil Sloane <njasloane@gmail.com> wrote:
A018805(n) is no. of pairs (x,y) in [1..n]X[1..n] with gcd(x,y)=1. It is ~ 6*n^2/Pi^2 + C*n*log n, I think. What is C, and how can one find it using Mathematica or some other program? I ask because there are several similar sums I am interested in. Is there a reference?
Background: A331755 has an explicit formula (involving A018805) and is ~ 9*n^4/(8*Pi^2) + O(n^3 log n). A331763 is a mystery that I would love to solve, and seems to be ~ constant*n^4/Pi^2. Maybe knowing the second terms in the asymptotic expansions would help with the curve-fitting. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun