Valeurs moyennes d'une fonction liée aux diviseurs d'un nombre entier

Let d(n) and d⁎(n) be the numbers of divisors and the numbers of unitary divisors of the integer n, and let S(x)=∑n≤xD(n)=∑n≤xd(n)d⁎(n)(x≥1). A divisor d of a integer n is called unitary if it is prime with nd. In this paper, we prove that S(x)∼Ax(x→+∞), where A=π26∏p(1−12p2+12p3)=1.4276565⋯, and for all x≥1, S(x)=Ax+R(x) such that|R(x)|≤32ζ(32)x12+54ζ(23)x13+O(x15).