

A264263


The number of distinct nontrivial integral cevians of an isosceles triangle, with base of length 1 and legs of length n, that divide the base into two integral parts.


2



0, 1, 1, 2, 2, 1, 3, 3, 1, 3, 3, 2, 5, 3, 1, 3, 7, 3, 3, 3, 1, 5, 5, 2, 5, 3, 3, 7, 3, 1, 5, 11, 3, 3, 3, 1, 5, 11, 3, 4, 4, 3, 7, 3, 3, 7, 7, 3, 5, 5, 1, 7, 7, 1, 3, 3, 3, 11, 11, 5, 5, 7, 3, 3, 3, 3, 15, 7, 1, 3, 7, 7, 11, 5, 1, 5, 11, 3, 3, 7, 3, 7, 7, 2
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OFFSET

1,4


COMMENTS

A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
A nontrivial cevian is one that does not coincide with a side of the triangle.
If a(n) = 1 then the length of the unique cevian is n^2.
It seems that a(n) = 1 if and only if n is the average of twin prime pairs divided by 2 (A040040).


LINKS



EXAMPLE

a(4) = 2 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts.


PROG

(PARI)
ceviso(n) = {
my(d, L=List());
for(k=1, n^2,
if(issquare(n^2+k^2k, &d) && d!=n,
listput(L, d)
)
);
Vec(L)
}
vector(100, n, #ceviso(n))


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



