Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 061.07904
Autor: Erdös, Pál
Title: On highly composite numbers. (In English)
Source: J. London Math. Soc. 19, 130-133 (1944).
Review: A (positive whole) number is called highly composite if it has more divisors than any smaller number, highly abundant if the sum of its divisors is greater than that for any smaller number, and superabundant if the sum of the reciprocals of its divisors is greater than that for any smaller number. The author uses {\it A.E.Ingham's} theorem on the difference between consecutive primes (Zbl 017.38904) to prove that if n is highly composite, there is another highly composite number between n and n+n(log n)-c, where c is a certain positive constant.
Reviewer: P.T.Bateman
Classif.: * 11A25 Arithmetic functions, etc.
Index Words: number theory
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