Estimates of certain sums involving reciprocals of the largest prime factor of an integer. (Chinese. English summary) Zbl 0684.10045
Let \(\sigma\) (n) denote the sum of all divisors of n, and \(\phi\) (n) denote Euler’s totient function. By using a method of P. Erdős, A. Ivić and C. Pomerance [Glas. Mat., III. Ser. 21(41), 283-300 (1986; Zbl 0615.10055)], the author establishes the asymptotic formulae for the sums \(\sum_{2\leq n\leq x}\sigma (n)/P(n)\) and \(\sum_{2\leq n\leq x}\phi (n)/P(n)\), where P(n) is the largest prime factor of n.
Reviewer: Lu Minggao
MSC:
11N37 | Asymptotic results on arithmetic functions |