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 A070090 Number of scalene integer triangles with perimeter n and prime side lengths. 5
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 4, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 3, 0, 2, 0, 1, 0, 3, 0, 4, 0, 1, 0, 6, 0, 4, 0, 5, 0, 6, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,35 LINKS R. Zumkeller, Integer-sided triangles FORMULA a(n) = A070088(n) - A070092(n). 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))) * A010051(i)_* A010051(k) * A010051(n-i-k). - Wesley Ivan Hurt, May 13 2019 EXAMPLE For n=15 there are A005044(15)=7 integer triangles: [1,7,7], [2,6,7], [3,5,7], [3,6,6], [4,4,7], [4,5,6] and [5,5,5]: three are scalene: [2<6<7], [3<5<7] and [4<5<6], but only one consists of primes, therefore a(15)=1. MATHEMATICA Table[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[n - i - k] - PrimePi[n - i - k - 1])*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 13 2019 *) CROSSREFS Cf. A070080, A070081, A070082, A070088, A005044, A070092, A070097, A070105, A070114. Sequence in context: A286351 A091394 A029881 * A230642 A053473 A322983 Adjacent sequences:  A070087 A070088 A070089 * A070091 A070092 A070093 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)