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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Large highly powerful numbers are cubeful


Authors: C. B. Lacampagne and J. L. Selfridge
Journal: Proc. Amer. Math. Soc. 91 (1984), 173-181
MSC: Primary 11A51
MathSciNet review: 740165
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Abstract: A number $ n = \prod\nolimits_{i = 1}^k {p_i^E} $ is called highly powerful if the product of the exponents $ E({p_i})$ of the primes is larger than that of any smaller number. If $ {p_k} > 19$, $ E({p_k}) = 3$. Further, we have developed an algorithm which finds all highly powerful numbers with $ E({p_k}) \ne 3$, and we list the 19 highly powerful numbers with $ E({p_k}) = 2$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740165-6
PII: S 0002-9939(1984)0740165-6
Article copyright: © Copyright 1984 American Mathematical Society