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A308074 Number of integer-sided triangles with perimeter n whose side lengths are mutually coprime. 4
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 5, 1, 2, 3, 5, 2, 8, 1, 5, 2, 5, 3, 12, 2, 7, 6, 12, 4, 16, 4, 12, 5, 11, 5, 22, 6, 16, 9, 18, 5, 25, 8, 20, 9, 18, 8, 39, 10, 22, 17, 29, 12, 42, 11, 32, 15, 37, 11, 49, 9, 32, 22, 41, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,18

LINKS

Table of n, a(n) for n=1..77.

FORMULA

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A236627 A116664 A295672 * A024161 A035156 A063883

Adjacent sequences:  A308071 A308072 A308073 * A308075 A308076 A308077

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 11 2019

STATUS

approved

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)