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A051493 Triangles with perimeter n and relatively prime integer side lengths. 16


%S 0,0,1,0,1,0,2,1,2,1,4,2,5,2,5,4,8,4,10,6,9,6,14,8,15,9,16,12,21,11,

%T 24,16,22,16,27,18,33,20,31,24,40,23,44,30,39,30,52,32,54,35,52,42,65,

%U 38,65,48,64,49,80,48,85,56,77,64,90,58,102,72,93,69,114,72,120,81

%N Triangles with perimeter n and relatively prime integer side lengths.

%C From _Peter Munn_, Jul 26 2017: (Start)

%C The triangles that meet the conditions are listed by nondecreasing n in A070110.

%C Without the requirement for relatively prime side lengths, this sequence becomes A005044.

%C Counting the triangles by longest side instead of perimeter, this sequence becomes A123323.

%C a(n) = A070094(n) + A070102(n) + A070109(n).

%C (End)

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Moebius transform of A005044.

%e There are 3 triangles with integer-length sides and perimeter 9: 1-4-4, 2-3-4, 3-3-3. 3-3-3 is omitted because isomorphic to 1-1-1, so a(9)=2.

%Y Cf. A005044, A057887, A070110, A123323.

%Y Equivalent sequences, restricted to subsets: A070091 (isosceles), A070094 (acute), A070102 (obtuse), A070109 (right-angled), A070138 (with integer area), A070202 (with integer inradius).

%K nonn

%O 1,7

%A _Neil Fernandez_

%E Corrected and extended with formula by _Christian G. Bower_, Nov 15 1999

%E Formula updated due to change to referenced sequence, and definition clarified by _Peter Munn_, Jul 26 2017

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Last modified July 9 00:55 EDT 2020. Contains 335537 sequences. (Running on oeis4.)