A259446 Number of triangles with sides pairwise relatively prime and no greater than n; permutations of sides are not considered distinct.

1, 1, 1, 1, 2, 2, 5, 7, 11, 12, 23, 25, 42, 48, 56, 65, 97, 103, 145, 157, 179, 194, 258, 270, 326, 351, 400, 425, 532, 544, 668, 719, 783, 828, 914, 941, 1121, 1180, 1271, 1316, 1541, 1571, 1821, 1902, 1998, 2085, 2387, 2442, 2705, 2787

Offset: 1

Author

Vincent J. Matsko, Jun 27 2015

Keywords

• nonn

Examples

			(1,1,1) is the only triangle up to n=4; (3,4,5) is added for n=5 and n=6.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

triangles[n_] := Module[{count = 0},
   For[a = 1, a <= n, a++,
    For[b = a, b <= n, b++,
     For[c = b, c <= n, c++,
      If[(a + b > c) && (b + c > a) && (c + a > b) && CoprimeQ[a, b, c],
       count++]]]];
   count];
triangles[#] & /@ Range[50]

PARI

a(n)=sum(a=3,n-2, sum(b=a+1,n-1, if(gcd(a,b)==1, sum(c=b+1,min(a+b-1,n), gcd(a*b,c)==1))))+1 \\ Charles R Greathouse IV, Jun 29 2015