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A024161 Number of integer-sided triangles with sides a,b,c, a < b < c, a+b+c = n such that a,b,c are pairwise relatively prime. 0
0, 0, 0, 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, 58, 12, 48, 19, 41, 18, 73, 19, 46, 30, 58, 22, 86, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,18

LINKS

Table of n, a(n) for n=1..91.

FORMULA

a(n) = Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/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. - Wesley Ivan Hurt, May 11 2019

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 + 1, Floor[(n - k - 1)/2]}], {k, Floor[(n - 1)/3]}], {n, 100}] (* Wesley Ivan Hurt, May 11 2019 *)

CROSSREFS

Sequence in context: A116664 A295672 A308074 * A035156 A063883 A079691

Adjacent sequences:  A024158 A024159 A024160 * A024162 A024163 A024164

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 25 06:19 EST 2022. Contains 350565 sequences. (Running on oeis4.)