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 A308308 Number of integer-sided triangles with perimeter n and at least one pair of side lengths that are not coprime. 0
 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 4, 6, 4, 8, 5, 10, 6, 11, 9, 13, 7, 15, 12, 16, 11, 19, 11, 23, 16, 25, 19, 27, 15, 31, 23, 31, 21, 36, 21, 40, 28, 43, 33, 47, 26, 50, 36, 52, 38, 60, 36, 62, 45, 66, 52, 72, 36, 75, 58, 74, 56, 84, 49, 91, 64, 93, 65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Wikipedia, Integer Triangle FORMULA a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * (1 - [gcd(i,k) * gcd(i,n-i-k) * gcd(k,n-i-k) = 1]), where [] is the Iverson bracket. a(n) = A005044(n) - A308074(n). MATHEMATICA Table[Sum[Sum[(1 - KroneckerDelta[GCD[i, k]*GCD[i, n - i - k]*GCD[k, n - i - k], 1])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] CROSSREFS Cf. A005044, A308074. Sequence in context: A130722 A308307 A147541 * A024162 A334677 A179080 Adjacent sequences:  A308305 A308306 A308307 * A308309 A308310 A308311 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 19 2019 STATUS approved

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)