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

56, 126, 252, 792, 116280, 203490, 2035800, 573166440, 818809200, 2310789600, 8597496600, 1889912732400

1

The theorem 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 all less than k and the prime factors of v are all at least as large as k. Then u > v holds in just 12 cases, namely the ones given above, which are the binomial coefficients (8,3), (9,4), (10,5), (12,5), (21,7), (21,8), (30,7), (33,13), (33,14), (36,13), (36,17), and (56,13). See S000072.

T. D. Noe, Plot of 12 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,full

T. D. Noe, Jun 02 2014