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On Abundant-Like Numbers

Published online by Cambridge University Press:  20 November 2018

Paul Erdös
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Problem 188, [3], stated: Apart from finitely many primes p show that if npis the smallest abundant number for which p is the smallest prime divisor of np then np is not squarefree.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 599 - 602
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Ramanujan, Srinivasa, Highly composite numbers, Collected papers Cambridge Univ. Press and Chelsea Publishing Company 78-128. See also L. Alaoglu and P. Erdös, On highly composite and similar numbers, Trans. Amer. Math. Soc. 56 (1944), 448-469 and J. L. Nicolas, Su Vordre maximum d'un ?l?ment dans le groupe Sn des permutations, Acta Arithmetica 14 (1968), 315-332.Google Scholar
2. Rosser, J.B. and Schoenfeld, L., Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.Google Scholar
3. Problem 188, Canad. Math. Bull. Vol. 14 (4), 1971.Google Scholar