linguistic:voice_change, linguistic:paraphrasing, information:extraction
Notation

In this article, ∑ p f (p) {\textstyle \sum _{p}f(p)} and ∏ p f (p) {\textstyle \prod _{p}f(p)} mean that the sum or product is over all prime numbers:

and

Similarly, ∑ p k f (p k) {\textstyle \sum _{p^{k}}f(p^{k})} and ∏ p k f (p k) {\textstyle \prod _{p^{k}}f(p^{k})} mean that the sum or product is over all prime powers with strictly positive exponent (so k = 0 is not included):

The notations ∑ d ∣ n f (d) {\textstyle \sum _{d\mid n}f(d)} and ∏ d ∣ n f (d) {\textstyle \prod _{d\mid n}f(d)} mean that the sum or product is over all positive divisors of n, including 1 and n. For example, if n = 12, then

The notations can be combined: ∑ p ∣ n f (p) {\textstyle \sum _{p\mid n}f(p)} and ∏ p ∣ n f (p) {\textstyle \prod _{p\mid n}f(p)} mean that the sum or product is over all prime divisors of n. For example, if n = 18, then

and similarly ∑ p k ∣ n f (p k) {\textstyle \sum _{p^{k}\mid n}f(p^{k})} and ∏ p k ∣ n f (p k) {\textstyle \prod _{p^{k}\mid n}f(p^{k})} mean that the sum or product is over all prime powers dividing n. For example, if n = 24, then