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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
DOI: https://doi.org/10.1090/S0002-9939-1984-0740165-6
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$.


References [Enhancements On Off] (What's this?)

  • [1] R. P. Brent, The first occurrence of large gaps between successive primes, Math. Comp. 27 (1973), 959-963. MR 0330021 (48:8360)
  • [2] H. C. Diamond, Elementary methods in the study of the distribution of prime numbers, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 553-589. MR 670132 (83m:10002)
  • [3] G. E. Hardy and M. V. Subbarao, Highly powerful numbers, Congr. Numer. 37 (1983), 277-307. MR 703589 (84h:10006)
  • [4] L. Schoenfeld, Sharper bounds for the Chebyshev functions. II, Math. Comp. 30 (1976), 337-360. MR 0457374 (56:15581b)

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DOI: https://doi.org/10.1090/S0002-9939-1984-0740165-6
Article copyright: © Copyright 1984 American Mathematical Society

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