Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A new function associated with the prime factors of $(^{n}_{k})$

Authors: E. F. Ecklund, P. Erdös and J. L. Selfridge
Journal: Math. Comp. 28 (1974), 647-649
MSC: Primary 10A20
MathSciNet review: 0337732
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $g(k)$ denote the least integer $> k + 1$ so that all the prime factors of $\left ( {\begin {array}{*{20}{c}} {g(k)} \\ k \\ \end {array} } \right )$ are greater than k. The irregular behavior of $g(k)$ is studied, obtaining the following bounds: ${k^{1 + c}} < g(k) < \exp (k(1 + o(1))).$ Numerical values obtained for $g(k)$ with $k \leqq 52$ are listed.

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

  • E. F. Ecklund Jr., On prime divisors of the binomial coefficient, Pacific J. Math. 29 (1969), 267–270. MR 244148
  • P. Erdös, "Some problems in number theory," in Computers in Number Theory, Academic Press, London, 1971, pp. 405-414.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10A20

Retrieve articles in all journals with MSC: 10A20

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society