A048688 Number of classes generated by function A000005 when applied to binomial coefficients.

1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 5, 8, 6, 6, 8, 9, 6, 11, 7, 11, 10, 10, 9, 11, 11, 11, 10, 15, 13, 15, 11, 15, 16, 14, 14, 16, 15, 15, 12, 18, 17, 18, 12, 22, 18, 20, 19, 21, 17, 20, 19, 24, 21, 21, 15, 25, 19, 18, 19, 24, 21, 28, 25, 26, 24, 29, 19, 29, 25, 24, 26, 29, 19

Offset

1,2

Links

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

Formula

a(n) = length(union(A000005(binomial(n,k)))), for 0<= k <= n.

Example

For n=9 A000005({C(9,k)})={1,3,9,12,12,12,12,9,3,1} includes 4 distinct values so generating 4 classes of k values: {0,9},{1,8},{2,7} and {3,4,5,6}. So a(9)=4.

Mathematica

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

Crossrefs

Cf. A000005, A001221, A007947.

Sequence in context: A074198 A196169 A330561 * A092695 A281687 A033270

Adjacent sequences: A048685 A048686 A048687 * A048689 A048690 A048691

Keyword

nonn

Author

Labos Elemer

Status

approved