Cases in a 1978 corollary of Ecklund, Eggleton, Erdos, and Selfridge.

56, 84, 120, 126, 252, 792, 816, 88560, 98280, 116280, 203490, 695520, 2035800, 177100560, 573166440, 818809200, 2310789600, 8597496600, 1889912732400

1

The corollary says: For positive integers n and k, with n >= 2k, let the binomial coefficient (n,k) = U*V, where the prime factors of U are at most k and the prime factors of V are all greater than k. Then U < V holds with just a finite number of exceptions, with 19 cases known, namely the ones given above, which are the binomial coefficients in S000071 and (9,3), (10,3), (18,3), (28,5), (54,7), (82,3), and (162,3).

T. D. Noe, Plot of 19 terms

E. F. Ecklund, Jr., R. B. Eggleton, P. Erdos, and J. L. Selfridge, On the prime factorization of binomial coefficients, J. Austral. Math. Soc. (Series A) 26 (1978), p. 257-269

nonn,fini

T. D. Noe, Jun 02 2014