“Erdös-Selfridge Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Erdös-Selfridge Function

释义

Erdös-Selfridge Function

The Erdös-Selfridge function is defined as the least integer bigger than such that all prime factorsof exceed (Ecklund et al. 1974). The best lower bound known is

(Granville and Ramare 1996). Scheidler and Williams (1992) tabulated

up to

, and Lukes et al. (1997) tabulated

for

. The values for

, 3, ... are 4, 7, 7, 23, 62, 143, 44, 159, 46, 47, 174, 2239, ...(Sloane's A046105).

See also Binomial Coefficient, Least Prime Factor

References

Ecklund, E. F. Jr.; Erdös, P.; and Selfridge, J. L. ``A New Function Associated with the prime factors of . Math. Comput. 28, 647-649, 1974.

Erdös, P.; Lacampagne, C. B.; and Selfridge, J. L. ``Estimates of the Least Prime Factor of a Binomial Coefficient.'' Math. Comput. 61, 215-224, 1993.

Granville, A. and Ramare, O. ``Explicit Bounds on Exponential Sums and the Scarcity of Squarefree Binomial Coefficients.'' Mathematika 43, 73-107, 1996.

Lukes, R. F.; Scheidler, R.; and Williams, H. C. ``Further Tabulation of the Erdös-Selfridge Function.'' Math. Comput. 66, 1709-1717, 1997.

Scheidler, R. and Williams, H. C. ``A Method of Tabulating the Number-Theoretic Function .'' Math. Comput. 59, 251-257, 1992.

Sloane, N. J. A. Sequence A046105in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

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