OFFSET
0,1
COMMENTS
The constant c in the asymptotic formulas Sum_{n1, n2 <= x} phi(lcm(n1, n2)) = c * x^4/4 + O(x^(7/2 + eps)) and Sum_{n1, n2 <= x} phi(lcm(n1, n2))/(n1*n2) = c * x^2 + O(x^(3/2 + eps)).
LINKS
Titus Hilberdink and László Tóth, On the average value of the least common multiple of k positive integers, Journal of Number Theory, Vol. 169 (2016), pp. 327-341. See p. 333.
EXAMPLE
0.33091829620850886597708997991322785489354334541048...
MATHEMATICA
$MaxExtraPrecision = 1500; m = 1500; c = LinearRecurrence[{-1, 2, 0, 1, -1}, {0, -6, 6, -22, 40}, m]; f[x_] := 1 - 3 x^2 + 2 x^3 - x^4 + 2 x^5 - x^6; Zeta[3] * f[1/2] * f[1/3] * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n] - 1/2^n - 1/3^n)/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]]
PROG
(PARI) zeta(3) * prodeulerrat(1 - 3/p^2 + 2/p^3 - 1/p^4 + 2/p^5 - 1/p^6)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Feb 18 2021
STATUS
approved