A020731 Numbers n for which number of distinct prime divisors of C(n,k) has maximum at k = [n/2].

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 47, 48, 49, 50, 55, 56, 57, 58, 63, 64, 65, 66, 67, 68, 71, 72, 73, 75, 76, 80, 83, 84, 85, 89, 90, 96, 97, 98, 99, 100, 107, 108, 109, 119

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			For n=21 the number of prime divisors of {C(21,k)} is {0,2,4,4,4,4,5,5,6,6,6,6,6,6,5,5,4,4,4,4,2,0}, the maximal value of 6 occurring at the central position.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A048486, A048299, A048484, A019491.

Programs

Mathematica

Select[Range[120], Function[n, ar = PrimeNu[Binomial[n, Range[0, n/2]]]; Max[ar] == ar[[-1]]]] (* Ivan Neretin, Aug 14 2015 *)