A019491 Numbers n for which number of distinct prime divisors of binomial(n,k) has local minimum at k = n/2.

10, 20, 27, 28, 29, 34, 38, 44, 45, 46, 51, 52, 53, 54, 60, 61, 62, 69, 70, 74, 77, 78, 79, 81, 82, 87, 88, 92, 93, 94, 95, 101, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 115, 116, 117, 118, 120, 122, 124, 125, 126, 127, 130, 138, 139, 140

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			If n=28 then {r(C(28,k))}={0,2,3,4,4,5,6,6,6,7,8,7,7,7,6,7,7,7,8,7,6,6,6,5,4,4,3,2,0}. Thus r(C(28,14))=6 is local minimum, while r(C(28,10))=8 is maximum.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A048484, A048486, A001221, A020731.

Programs

Mathematica

Select[Range[140], MatchQ[PrimeNu[Binomial[#, Range[Floor[#/2], #]]], {(x_) .., y_, _} /; x < y]&] (* Jean-François Alcover, Dec 10 2016 *)

Extensions

Data corrected by Jean-François Alcover, Dec 10 2016