A048687 - OEIS

%I #20 May 19 2018 02:25:01

%S 1,2,2,3,3,2,3,4,4,4,5,4,4,4,4,5,6,5,6,6,5,6,7,5,6,6,8,8,8,6,7,9,7,9,

%T 9,8,8,9,10,8,10,8,9,11,8,9,10,9,10,10,10,9,11,10,12,11,12,11,13,11,

%U 12,12,12,13,13,12,14,13,14,12,14,13,13,13,13,13,12,15,15,14,16,14,16,14

%N a(n) is the number of classes generated by function A001221 when applied to binomial coefficients.

%H G. C. Greubel, <a href="/A048687/b048687.txt">Table of n, a(n) for n = 1..1000</a>

%e For n=9, A001221({binomial(9,k)})={0,1,2,3,3,3,3,2,1,0} includes 4 distinct values. Therefore, a(9) = 4.

%t Table[Length[Union[Table[PrimeNu[Binomial[n, k]], {k, 0, n}]]], {n, 1, 100}] (* _G. C. Greubel_, Apr 24 2017 *)

%o (PARI) a(n) = #Set(vector(n+1, k, omega(binomial(n, k-1)))); \\ _Michel Marcus_, May 14 2018

%Y Cf. A001221, A007947.

%K nonn

%O 1,2

%A _Labos Elemer_