##
**Zentralblatt MATH**

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

**Zbl.No: ** 536.10007

**Autor: ** Erdös, Paul; Guy, R.K.; Selfridge, J.L.

**Title: ** Another property of 239 and some related questions. (In English)

**Source: ** Numerical mathematics and computing, Proc. 11th Manitoba Conf., Winnipeg/Manit. 1981, Congr. Numerantium 34, 243-257 (1982).

**Review: ** [For the entire collection see Zbl 532.00008.]

Regarding the decomposition n! = a_{1}a_{2}...a_{k} of n! into k factors the authors prove the following three interesting theorems:

Theorem 1. If n > 239 there is no factorization with n < a_{1} < a_{2} < ... < a_{k} \leq 2n.

Theorem 2. For every n > 13 there is a factorization with n < a_{1} \leq a_{2} \leq ... \leq a_{k} \leq 2n.

Theorem 3. Let f(n) denote the smallest integer a_{k} for which there exists a factorization with n < a_{1} < a_{2} < ... < a_{k}. Then there are constants 0 < c_{1} < c_{2} such that 2n+c_{1} n/ log n < f(n) < 2n+c_{2} n/ log n. Besides they ask many interesting open questions.

**Reviewer: ** K.Ramachandra

**Classif.: ** * 11A25 Arithmetic functions, etc.

11A41 Elemementary prime number theory

05A10 Combinatorial functions

**Keywords: ** factors of n factorial

**Citations: ** Zbl 532.00008

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag