A048299 Let b(n) = A048273(n) = maximal number of prime factors of C(n,k) for k=0..n; sequence gives smallest value of k achieving b(n).

0, 1, 1, 2, 2, 1, 2, 4, 3, 4, 4, 6, 6, 5, 4, 8, 8, 6, 6, 8, 8, 8, 8, 10, 5, 6, 12, 10, 10, 9, 10, 12, 12, 16, 15, 16, 16, 18, 18, 20, 20, 18, 18, 20, 16, 13, 16, 19, 20, 15, 20, 17, 18, 21, 24, 20, 21, 21, 21, 28, 29, 21, 21, 32, 32, 28, 29, 32, 32, 32, 28, 28, 29, 32, 32, 32, 35, 32

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			For n = 50, the number of distinct prime factors of C(50, k) can be 0,2,3,4,5,6,7,8,9,10. The maximum is reached at several positions k=15,17,...,33,35. Thus a(50) = 15, far from the central C(50, 25).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A048273, A001405, A048571.

Programs

Mathematica

Table[Min@ MaximalBy[Range[0, n], PrimeNu@ Binomial[n, #] &], {n, 78}] (* Michael De Vlieger, Aug 01 2017 *)