A048689 Number of classes generated by function A001222 when applied to binomial coefficients.

1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 8, 7, 7, 7, 8, 8, 8, 8, 9, 8, 9, 9, 10, 9, 10, 11, 10, 10, 11, 9, 10, 11, 11, 12, 12, 12, 12, 10, 12, 11, 12, 13, 11, 13, 14, 13, 12, 12, 13, 13, 14, 11, 14, 13, 14, 14, 12, 13, 16, 15, 14, 14, 15, 14, 16, 13, 17, 15, 14, 16

Offset

1,2

Links

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

Formula

a(n) = length(union(A001222(binomial(n,k)))), for 0 <= k <= n.

Example

For n=9, A001222({C(9,k)}) = {0,2,4,4,4,4,4,4,2,0} includes 3 distinct values, thus generating 3 classes of k values: {0,9},{1,8} and {2,3,4,5,6,7}. So a(9)=3.

Mathematica

Table[Length[Union[Table[PrimeOmega[Binomial[n, k]], {k, 0, n}]]], {n,
   1, 50}] (* G. C. Greubel, May 19 2017 *)

Crossrefs

Cf. A000005, A001221, A007947, A001222.

Sequence in context: A127240 A097561 A162345 * A069923 A095840 A131343

Adjacent sequences: A048686 A048687 A048688 * A048690 A048691 A048692

Keyword

nonn

Author

Labos Elemer

Status

approved