Further tabulation of the Erdös-Selfridge function

Authors:
Richard F. Lukes, Renate Scheidler and Hugh C. Williams

Journal:
Math. Comp. **66** (1997), 1709-1717

MSC (1991):
Primary 11N25, 11Y70, 11-04

MathSciNet review:
1422791

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Abstract: For a positive integer , the Erdös-Selfridge function is the least integer such that all prime factors of exceed . This paper describes a rapid method of tabulating using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of . A table of values of for is provided.

**1.**Renate Scheidler and Hugh C. Williams,*A method of tabulating the number-theoretic function 𝑔(𝑘)*, Math. Comp.**59**(1992), no. 199, 251–257. MR**1134737**, 10.1090/S0025-5718-1992-1134737-X**2.**E. F. Ecklund Jr., P. Erdös, and J. L. Selfridge,*A new function associated with the prime factors of (ⁿ_{𝑘})*, Math. Comp.**28**(1974), 647–649. MR**0337732**, 10.1090/S0025-5718-1974-0337732-2**3.**P. Erdős, C. B. Lacampagne, and J. L. Selfridge,*Estimates of the least prime factor of a binomial coefficient*, Math. Comp.**61**(1993), no. 203, 215–224. MR**1199990**, 10.1090/S0025-5718-1993-1199990-6**4.**R. F. Lukes, C. D. Patterson, and H. C. Williams,*Numerical sieving devices: their history and some applications*, Nieuw Arch. Wisk. (4)**13**(1995), no. 1, 113–139. MR**1339041****5.**A. Granville and O. Ramaré,*Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients*, Mathematika,**43**(1996), 73-107. CMP**96:16****6.**Leonard Eugene Dickson,*History of the theory of numbers. Vol. I: Divisibility and primality.*, Chelsea Publishing Co., New York, 1966. MR**0245499**

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Additional Information

**Richard F. Lukes**

Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Email:
rflukes@cs.umanitoba.ca

**Renate Scheidler**

Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716

Email:
scheidle@math.udel.edu

**Hugh C. Williams**

Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Email:
hugh_williams@csmail.cs.umanitoba.ca

DOI:
http://dx.doi.org/10.1090/S0025-5718-97-00864-8

Received by editor(s):
October 18, 1994

Received by editor(s) in revised form:
October 9, 1995, and August 21, 1996

Additional Notes:
The third author’s research is supported by NSERC of Canada grant A7649

Article copyright:
© Copyright 1997
American Mathematical Society