A286980 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).

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

Offset

1,1

Comments

The corresponding pairs (n,k) are: (8,3), (9,4), (10,5), (12,5), (21,7), (21,8), (30,7), (33,13), (33,14), (36,13), (36,17), (56,13).

Subsequence of A286981.

Links

Table of n, a(n) for n=1..12.

Earl F. Ecklund, Jr., Roger B. Eggleton, Paul Erdős 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.

Example

56 = Binomial(8,3) = 8*7, gpf(8) = 2 < 3 and gpf(7) = 7 >= 3, and 8 > 7, thus 56 is in the sequence.

Crossrefs

Cf. A007318, A286981.

Sequence in context: A157330 A038849 A003781 * A254463 A030443 A135803

Adjacent sequences: A286977 A286978 A286979 * A286981 A286982 A286983

Keyword

nonn,fini,full

Author

Amiram Eldar, May 17 2017

Status

approved