

A308212


Number of integersided triangles with perimeter n and sides a, b and c such that a <= b <= c and the length of side a is coprime to b.


1



0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 2, 4, 2, 3, 2, 5, 3, 6, 6, 8, 4, 8, 7, 10, 6, 9, 8, 13, 11, 16, 15, 18, 12, 16, 15, 21, 15, 19, 17, 24, 20, 27, 26, 30, 22, 30, 29, 36, 30, 35, 33, 42, 36, 42, 40, 46, 36, 46, 44, 54, 44, 50, 47, 55, 49, 60, 58, 65, 57, 69
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OFFSET

1,9


LINKS

Table of n, a(n) for n=1..71.
Wikipedia, Integer Triangle


FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((nk)/2)} sign(floor((i+k)/(nik+1))) * [gcd(k,i) = 1], where [] is the Iverson bracket.


MATHEMATICA

Table[Sum[Sum[Floor[1/GCD[k, i]] Sign[Floor[(i + k)/(n  i  k + 1)]], {i, k, Floor[(n  k)/2]}], {k, Floor[n/3]}], {n, 100}]


CROSSREFS

Cf. A308211.
Sequence in context: A157898 A137430 A262138 * A181346 A300815 A002121
Adjacent sequences: A308209 A308210 A308211 * A308213 A308214 A308215


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, May 15 2019


STATUS

approved



