Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  446.10033
Autor:  Erdös, Paul; Nicolas, J.L.
Title:  Grandes valeurs d'une fonction liée au produit d'entiers consecutifs. (Large values on a function related to the product of consecutive integers.) (In French)
Source:  Publ. Math. Orsay 81.01, 30-34 (1981).
Review:  Let f(n) = max{k; n in P(m,k); 1 \leq m \leq n; 1 \leq k \leq n} where n in P(m,k) means that n divides A = (m+1)...(m+k) but does not divide A/(m+i) for i = 1,...,k. The authors state without proofs several interesting results about the arithmetical functions f(n), among which are 1) sumn \leq xf(n) = (1+o(1))x log log x, 2) the maximal order of f(n) equals

\frac{e\gamma/2 log n}{2(log log n) ½}+\frac{\gamma e\gamma log n}{4 log log n}(1+o(1)),

where \gamma denotes Euler's constant.
Reviewer:  A.Ivic
Classif.:  * 11N37 Asymptotic results on arithmetic functions
                   11A25 Arithmetic functions, etc.
Keywords:  asymptotic order; Euler's constant; linear sieve; highly composite numbers; product of consecutive integers

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