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 A051493 Triangles with perimeter n and relatively prime integer side lengths. 16
 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, 24, 16, 22, 16, 27, 18, 33, 20, 31, 24, 40, 23, 44, 30, 39, 30, 52, 32, 54, 35, 52, 42, 65, 38, 65, 48, 64, 49, 80, 48, 85, 56, 77, 64, 90, 58, 102, 72, 93, 69, 114, 72, 120, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS From Peter Munn, Jul 26 2017: (Start) The triangles that meet the conditions are listed by nondecreasing n in A070110. Without the requirement for relatively prime side lengths, this sequence becomes A005044. Counting the triangles by longest side instead of perimeter, this sequence becomes A123323. a(n) = A070094(n) + A070102(n) + A070109(n). (End) LINKS N. J. A. Sloane, Transforms FORMULA Moebius transform of A005044. EXAMPLE 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. CROSSREFS Cf. A005044, A057887, A070110, A123323. Equivalent sequences, restricted to subsets: A070091 (isosceles), A070094 (acute), A070102 (obtuse), A070109 (right-angled), A070138 (with integer area), A070202 (with integer inradius). Sequence in context: A160974 A187718 A029196 * A029173 A002331 A060805 Adjacent sequences:  A051490 A051491 A051492 * A051494 A051495 A051496 KEYWORD nonn AUTHOR EXTENSIONS Corrected and extended with formula by Christian G. Bower, Nov 15 1999 Formula updated due to change to referenced sequence, and definition clarified by Peter Munn, Jul 26 2017 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)