%I #19 Dec 10 2016 19:35:57
%S 0,0,1,0,2,1,2,2,2,2,2,1,2,2,5,4,2,2,2,2,5,2,2,5,4,2,3,2,2,5,2,6,5,2,
%T 8,2,2,2,5,8,2,5,2,2,8,2,2,9,4,4,5,2,2,3,8,8,5,2,2,5,2,2,8,8,8,5,2,2,
%U 5,8,2,8,2,2,9,2,8,5,2,14,4,2,2,5,8,2
%N The number of distinct lengths of nontrivial integral cevians of an equilateral triangle of side n that divide an edge into two integral parts.
%C A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
%C A nontrivial cevian is one that does not coincide with a side of the triangle.
%C For an equilateral triangle of side n, the lengths of its cevians are the values of y in the solutions to x^2y^2n*x+n^2=0.
%H Colin Barker, <a href="/A246920/b246920.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cevian">Cevian</a>
%e a(15) = 5 because cevians of an equilateral triangle of side 15 have length 13, 21, 35, 57 or 169.
%o (PARI)
%o \\ Returns the number of cevians of an equilateral triangle of side n.
%o count(n) = {
%o s=[];
%o n=12*n^2;
%o fordiv(n, f,
%o g=n\f;
%o if(f<=g && (f+g)%2==0,
%o x=(f+g)\2;
%o if(x%4==0,
%o s=concat(s, x\4)
%o )
%o )
%o );
%o Colrev(s)~
%o }
%o vector(100, n, #count(n)1)
%Y Cf. A229839, A246918, A246919.
%K nonn
%O 1,5
%A _Colin Barker_, Sep 07 2014
