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! = a1a2...ak of n! into k factors the authors prove the following three interesting theorems:
Theorem 1. If n > 239 there is no factorization with n < a1 < a2 < ... < ak \leq 2n.
Theorem 2. For every n > 13 there is a factorization with n < a1 \leq a2 \leq ... \leq ak \leq 2n.
Theorem 3. Let f(n) denote the smallest integer ak for which there exists a factorization with n < a1 < a2 < ... < ak. Then there are constants 0 < c1 < c2 such that

2n+c1 n/ log n < f(n) < 2n+c2 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

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