Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

A method of tabulating the number-theoretic function $ g(k)$


Authors: Renate Scheidler and Hugh C. Williams
Journal: Math. Comp. 59 (1992), 251-257
MSC: Primary 11Y70; Secondary 11N36
DOI: https://doi.org/10.1090/S0025-5718-1992-1134737-X
MathSciNet review: 1134737
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ g(k)$ be the least integer $ > k + 1$ such that all prime factors of $ \left( {\begin{array}{*{20}{c}} {g(k)} \\ k \\ \end{array} } \right)$ are greater than k. The function $ g(k)$ appears to show quite irregular behavior and is hard to compute. This paper describes a method of computing $ g(k)$, using sieving techniques, and provides a table of values of $ g(k)$ for $ k \leq 140$.


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

  • [1] L. E. Dickson, History of the theory of numbers, vol. 1, Chelsea, New York, 1966.
  • [2] E. F. Ecklund, Jr., P. Erdős, and J. L. Selfridge, A new function associated with the prime factors of $ \left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array} } \right)$, Math. Comp. 28 (1974), pp. 647-649.
  • [3] P. Erdős, Some problems in number theory, Computers in Number Theory (A. O. L. Atkin and B. J. Birch, eds.), Academic Press, London, 1971, pp. 405-414.
  • [4] -, Uses of and limitations of computers in number theory, Computers in Mathematics (D. V. Chudnovsky and R. D. Jenks, eds.), Marcel Dekker, New York, 1990, pp. 241-260. MR 1068538 (91k:11112)
  • [5] A. J. Stephens and H. C. Williams, An open architecture number sieve, London Math. Soc. Lecture Note Ser., vol. 154, Cambridge Univ. Press, 1990, pp. 38-75. MR 1055399

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11Y70, 11N36

Retrieve articles in all journals with MSC: 11Y70, 11N36


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1992-1134737-X
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society