A048275 a(n) = maximal value for number of divisors of C(n,k) for k=0..n.

1, 2, 2, 4, 4, 6, 4, 8, 12, 18, 16, 24, 24, 32, 24, 48, 32, 60, 48, 80, 96, 128, 64, 160, 192, 192, 288, 480, 384, 480, 192, 576, 768, 768, 1024, 1536, 1152, 1536, 1536, 2304, 1536, 2880, 2304, 2560, 3072, 3840, 2304, 3456, 3840, 5184, 6144, 9216, 5120

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			If n=20, then the number of divisors of C(20,k) is one of {1,6,8,16,24,40,48,64,80}, so a(20) = 80.
		

Links

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

Crossrefs

Cf. A000005, A001405, A034974.

Programs

Mathematica

Table[Max@ Map[DivisorSigma[0, #] &, Binomial[n, Range[0, n]]], {n, 53}] (* Michael De Vlieger, Mar 05 2017 *)

PARI

a(n) = vecmax(vector(n+1, k, numdiv(binomial(n,k-1)))); \\ Michel Marcus, Mar 05 2017