Analytic study of norms of prime partitions (Q2046125)

Considering an ordinary partition of the positive integer \(n\), the product of its parts is called the norm of the partition as suggested by \textit{R. Schneider} and \textit{A. V. Sills} [Integers 20A, Paper A13, 16 p. (2020; Zbl 1458.11144)]. Prime partitions are partitions of integers into prime parts. For their number, see \textit{R. C. Vaughan} [Ramanujan J. 15, No. 1, 109--121 (2008; Zbl 1154.11035)]. In the paper under review the author studies norms of prime partitions. Let \(r_p(i, n)\) denote the number of times \(i\) appears as a norm in the prime partitions of \(n\). The author gives the generating function of \(r_p(i, n)\) with consequences and recursive relations on certain weighted sums on \(r_p(i, n)\) too.