On the mean value of the enumeration function for multiplicative partitions. (English) Zbl 0694.10044
Denote by g(n) the number of multiplicative partitions of the positive integer n. Using N. G. de Bruijn’s result on the number of positive integers \(\leq x\) and free of prime factors \(>y\) [Indagationes Math. 13, 50-60 (1951; Zbl 0042.042)] the authors give an upper bound for \(\sum_{n\leq x}g(n)\). A better result and further references may be found in the paper of E. R. Canfield, P. Erdős and C. Pomerance [J. Number Theory 17, 1-28 (1983; Zbl 0513.10043)], where an asymptotic formula for \(\sum_{n\leq x}g(n)\) is derived.
Reviewer: T.Maxsein
References:
| [1] | Titchmarsh, The theory of the Riemann Zeta–Function (1951) · Zbl 0042.07901 |
| [2] | de Bruijn, Indag. Math. 13 pp 50– (1951) · doi:10.1016/S1385-7258(51)50008-2 |
| [3] | Xiao-Xia, Acta Math. Sinica 30 pp 268– (1987) |
| [4] | DOI: 10.2307/2975729 · Zbl 0523.10007 · doi:10.2307/2975729 |
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