

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
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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

Table of n, a(n) for n=1..74.
N. J. A. Sloane, Transforms


FORMULA

Moebius transform of A005044.


EXAMPLE

There are 3 triangles with integerlength sides and perimeter 9: 144, 234, 333. 333 is omitted because isomorphic to 111, so a(9)=2.


CROSSREFS

Cf. A005044, A057887, A070110, A123323.
Equivalent sequences, restricted to subsets: A070091 (isosceles), A070094 (acute), A070102 (obtuse), A070109 (rightangled), 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

Neil Fernandez


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



