A060567 - OEIS

%I #10 Jul 20 2024 20:19:49

%S 3,2,1,2,2,2,4,2,2,6,5,4,10,4,2,8,10,6,12,4,6,18,10,4,14,14,6,10,23,

%T 20,22,10,18,22,10,18,34,26,15,18,24,14,32,14,10,42,28,12,28,18,12,32,

%U 34,14,25,26,42,54,30,14,58,42,22,24,28,36,60,38,20,34,44,26,70,42,20,42

%N Number of binomial coefficients C(n,j) with j=0..n that are divisible by C(n,2).

%F a(n) = Cardinality{j | C(n,2) divides C(n,j), j=0..n}.

%e The relevant residues C(n,j) mod C(n,2) for n=16 are {1, 16, 0, 80, 20, 48, 88, 40, 30, 40, 88, 48, 20, 80, 0, 16, 1}, so a(16) = 2.

%e For n=227, there are only 6 nonzero residues; the residues are {1, 227, [111 zeros], 454, 454, [111 zeros], 227, 1}, so a(227) = 222.

%Y Cf. A060430, A014070.

%K nonn

%O 2,1

%A _Labos Elemer_, Apr 12 2001