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

1,5

Links

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

Example

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

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]

Prog

(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

Crossrefs

Sequence in context: A239737 A262883 A308908 * A265769 A308957 A240488

Adjacent sequences: A259443 A259444 A259445 * A259447 A259448 A259449

Keyword

nonn

Author

Vincent J. Matsko, Jun 27 2015

Status

approved