Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 061.07903
Autor: Alaoglu, Leon; Erdös, Pál
Title: On highly composite and similar numbers. (In English)
Source: Trans. Am. Math. Soc. 56, 448-469 (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 obtain various results about these classes of numbers.
Classif.: * 11A25 Arithmetic functions, etc.
Index Words: number theory
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