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 A286981 Binomial coefficients binomial(n,k) = UV such that n>=2k and U > V, where gpf(U) <= k, gpf(V) > k (gpf(n)= is the greatest prime factor of n). 1
 56, 84, 120, 126, 252, 792, 816, 88560, 98280, 116280, 203490, 695520, 2035800, 177100560, 573166440, 818809200, 2310789600, 8597496600, 1889912732400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding pairs (n,k) are: (8,3), (9,3), (10,3), (9,4), (10,5), (12,5), (18,3), (82,3), (28,5), (21,7), (21,8), (162,3), (30,7), (54,7), (33,13), (33,14), (36,13), (36,17), (56,13). Ecklund et al. proved that the sequence is finite, and that these are the only terms, except for the cases k = 3, 5 and 7, but they strongly conjectured that the list is complete. They also give the near miss binomial(514,3)=22500864=UV, with U=2^9*3^2=4608, V=19*257=4883, and V/U < 1.06. No other terms below 10^20. Supersequence of A286980. LINKS Earl F. Ecklund, Jr., Roger B. Eggleton, Paul ErdÅ‘s and John L. Selfridge, On the prime factorization of binomial coefficients, Journal of the Australian Mathematical Society (Series A), Vol. 26, No. 3 (1978), pp. 257-269. Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, 2004, B31, p. 130. EXAMPLE 84 = Binomial(9,3) = 12*7, gpf(12) = 3 <= 3 and gpf(7) = 7 > 3, and 12 > 7, thus 84 is in the sequence. CROSSREFS Cf. A007318, A286980. Sequence in context: A039335 A043938 A214250 * A254369 A234927 A104394 Adjacent sequences:  A286978 A286979 A286980 * A286982 A286983 A286984 KEYWORD nonn,fini AUTHOR Amiram Eldar, May 17 2017 STATUS approved

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Last modified October 20 06:51 EDT 2018. Contains 316378 sequences. (Running on oeis4.)