Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 May 20 2018 12:39:38
%S 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,
%T 16,14,14,14,15,16,19,18,18,18,21,19,22,21,22,23,24,24,24,22,24,25,27,
%U 23,25,24,25,29,29,28,31,31,32,30,28,29,33,31,32,34,36,35,37,36,35,36
%N Number of classes generated by function A007947 when applied to binomial coefficients.
%e 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.
%t a[n_] = Length[ Union[ Table[ A007947[ binomial[ n, k ] ], {k, 0, n} ] ] ]
%o (PARI) a(n) = #Set(vector(ceil(n\2)+1, k, factorback(factorint(binomial(n,k-1))[, 1]))); \\ _Michel Marcus_, May 20 2018
%Y Cf. A007947, A080396.
%K nonn
%O 1,2
%A _Labos Elemer_