Further tabulation of the Erdös-Selfridge function

For a positive integer k, the Erdos-Selfridge function is the least integer g(k) > k + 1 such that all prime factors of ( g k (k) ) exceed k. This paper describes a rapid method of tabulating g(k) 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 g(k). A table of values of g(k) for 135 ≤ k ≤ 200 is provided.