A048686 Number of classes generated by function A007947 when applied to binomial coefficients.

1, 2, 2, 3, 3, 4, 4, 4, 4, 6, 6, 6, 7, 8, 8, 9, 8, 10, 8, 10, 11, 12, 12, 12, 13, 12, 12, 15, 15, 16, 14, 14, 14, 15, 16, 19, 18, 18, 18, 21, 19, 22, 21, 22, 23, 24, 24, 24, 22, 24, 25, 27, 23, 25, 24, 25, 29, 29, 28, 31, 31, 32, 30, 28, 29, 33, 31, 32, 34, 36, 35, 37, 36, 35, 36

Offset

1,2

Links

Table of n, a(n) for n=1..75.

Example

For n=9, A007947({C(9,k)}) = {1,3,6,42,42,42,42,6,3,1} includes 4 distinct values, thus generating 4 classes of k values: {0,9}, {1,8}, {2,7} and {3,4,5,6}. So a(9)=4.

Mathematica

a[n_] = Length[ Union[ Table[ A007947[ binomial[ n, k ] ], {k, 0, n} ] ] ]

Prog

(PARI) a(n) = #Set(vector(ceil(n\2)+1, k, factorback(factorint(binomial(n, k-1))[, 1]))); \\ Michel Marcus, May 20 2018

Crossrefs

Cf. A007947, A080396.

Sequence in context: A074794 A234309 A306921 * A278959 A090501 A361385

Adjacent sequences: A048683 A048684 A048685 * A048687 A048688 A048689

Keyword

nonn

Author

Labos Elemer

Status

approved