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.