Baker's dozen digits of two sums involving reciprocal products of an integer and its greatest prime factor

Abstract

Two sums over the inverse of the product of an integer n and its greatest prime factor G(n), are computed to first 13 decimal digits. These sums converge, but converge very slowly. They are transformed into sums involving Mertens' prime product with the remainder term which are estimated by means of Chebyshev's {\theta}-function.