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 A308255 Sum of the smallest side lengths of all integer-sided triangles with perimeter n and nonprime sides. 0
 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 4, 1, 4, 0, 4, 1, 10, 5, 10, 11, 20, 10, 24, 19, 32, 23, 35, 24, 51, 36, 53, 54, 74, 46, 73, 56, 91, 63, 89, 64, 121, 91, 136, 136, 173, 109, 168, 133, 202, 189, 232, 204, 290, 270, 318, 328, 381, 293, 375, 356, 435, 365, 436 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 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))) * A005171(i) * A005171(k) * A005171(n-i-k) * k. MATHEMATICA Table[Sum[Sum[k*(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - i - k] + PrimePi[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. A005171, A308253. Sequence in context: A171539 A106141 A082999 * A333240 A010641 A165486 Adjacent sequences:  A308252 A308253 A308254 * A308256 A308257 A308258 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 17 2019 STATUS approved

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)