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 A308069 Number of integer-sided triangles with perimeter n whose side lengths are semiprime. 1
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 3, 4, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 4, 4, 2, 2, 2, 3, 4, 4, 5, 5, 4, 7, 6, 4, 2, 3, 5, 4, 2, 2, 3, 3, 3, 5, 8, 6, 6, 7, 7, 8, 7, 7, 10, 9, 9, 10, 12, 14, 10, 7, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,22 LINKS Table of n, a(n) for n=1..85. 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))) * c(i) * c(k) * c(n-i-k), where c is the semiprime characteristic (A064911). MATHEMATICA Table[Sum[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[k], 2] KroneckerDelta[PrimeOmega[n - i - k], 2]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] CROSSREFS Cf. A064911. Sequence in context: A337277 A269974 A269975 * A161895 A048138 A165022 Adjacent sequences: A308066 A308067 A308068 * A308070 A308071 A308072 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 10 2019 STATUS approved

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Last modified August 14 13:35 EDT 2024. Contains 375165 sequences. (Running on oeis4.)