## Erdös-Selfridge Function

The Erdös-Selfridge function is defined as the least integer bigger than such that all prime factors of 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).

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 A046105 in The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.