A123325 Number of distinct angles in all integer-sided triangles with all sides <= n.

1, 3, 9, 17, 35, 49, 82, 109, 149, 188, 262, 316, 419, 500, 607, 698, 876, 1004, 1222, 1383, 1589, 1782, 2108, 2318, 2634, 2914, 3253, 3564, 4088, 4411, 5000, 5392, 5917, 6410, 6995, 7468, 8308, 8926, 9661, 10268, 11313, 11976, 13136, 13951, 14875

Offset: 1

Author

Franklin T. Adams-Watters, Sep 25 2006

Keywords

• nonn

Comments

Using the law of cosines, the angle A opposite side a has cos A = (b^2 + c^2 - a^2) / (2bc) and the cosine uniquely identifies an angle of a triangle.

Crossrefs

Cf. A123323, A123324.

Programs

PARI

A123325(n)=local(i,j,k,l); r=0; l=listcreate(n^3); for(i=1,n, for(j=1,n, for(k=1,n, if(gcd(i,gcd(j,k))==1&&2*max(i,max(j,k))