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The square-full numbers in an interval

Published online by Cambridge University Press:  24 October 2008

M. N. Huxley  and
O. Trifonov
M. N. Huxley
Affiliation:
School of Mathematics, University of Wales College of Cardiff, 23 Senghennydd Rd., Cardiff, CF2 4YH
O. Trifonov
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, 1113 Sofiaˇ, Bulgaria
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Extract

A positive integer is square-full if each prime factor occurs to the second power or higher. Each square-full number can be written uniquely as a square times the cube of a square-free number. The perfect squares make up more than three-quarters of the sequence {si} of square-full numbers, so that a pair of consecutive square-full numbers is a pair of consecutive squares at least half the time, with

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 2 , February 1996 , pp. 201 - 208
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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