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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 403.10004

**Autor: ** Erdös, Paul; Loxton, J.H.

**Title: ** Some problems in partitio numerorum. (In English)

**Source: ** J. Aust. Math. Soc., Ser. A 27, 319-331 (1979).

**Review: ** The paper investigates asymptotic results for certain partition problems in which the parts are restricted by divisibility conditions. For example, let p(n) be the number of partitions n = a_{1}+...+a_{k} into positive integers with a_{1}|a_{2}|...|a_{k} and let q(n) be the number of these partitions with distinct parts. We find that p(n) behaves like the binary partition function which counts partitions into powers of 2 and can be estimated precisely. The behaviour of q(n) is less amenable to analysis and leads to questions on the distribution of primes in sequences of the shape 2^{a}m+1.

**Classif.: ** * 11P81 Elementary theory of partitions

11N05 Distribution of primes

00A07 Problem books

**Keywords: ** partition; divisibility conditions; distribution of primes

**Index Words: ** Problems

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