In this paper we study how often the divisor function lies in a set $〈P〉$ generated by a subset P of the primes by multiplication. We consider a variety of different sets P using results on the average behaviour of multiplicative functions by Wirsing and Delange. In particular, we find out how often $d(n)$ is a power of a given integer. The methods apply more generally to non-negative integer valued multiplicative functions.

中文翻译：

---

d(n) 多久是给定整数的幂？

在本文中，我们研究除数函数在一个集合中的频率$〈磷〉$由素数的子集P通过乘法生成。我们使用 Wirsing 和 Delange 关于乘法函数平均行为的结果来考虑各种不同的集合P。特别是，我们发现多久$d(n)$是给定整数的幂。这些方法更普遍地应用于非负整数值乘法函数。