Erdős-Selfridge Function

The Erdős-Selfridge function  is defined as the least integer bigger than  such that the least prime factor of  exceeds , where  is the binomial coefficient (Ecklund et al. 1974, Erdős et al. 1993). 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 , 2, 3, ... are 3, 6, 7, 7, 23, 62, 143, 44, 159, 46, 47, 174, 2239, ... (OEIS A003458).

REFERENCES:

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

Erdős, 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 Erdős-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 A003458/M2515 in "The On-Line Encyclopedia of Integer Sequences."