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 A308451 Number of integer-sided triangles with perimeter n whose largest side length is prime. 3
 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 3, 2, 2, 1, 5, 3, 3, 2, 2, 1, 1, 0, 6, 5, 5, 4, 11, 9, 9, 7, 7, 5, 5, 3, 12, 10, 10, 8, 18, 15, 15, 13, 13, 11, 11, 9, 21, 18, 18, 15, 15, 12, 12, 10, 10, 8, 8, 6, 21, 19, 19, 17, 33, 30, 30, 27, 27, 24, 24, 21, 21, 19, 19, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 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(n-i-k), where c(n) is the prime characteristic (A010051). MAPLE f:= proc(n) local p, v; v:= add(1/2*(3*p-n+1)+`if`((n-p)::even, 1/2, 0), p = select(isprime, [\$ceil(n/3)..floor((n-1)/2)])); end proc: map(f, [\$1..100]); # Robert Israel, May 28 2019 MATHEMATICA Table[Sum[Sum[ (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. A010051, A308450. Sequence in context: A334204 A336362 A336363 * A308067 A124748 A161225 Adjacent sequences: A308448 A308449 A308450 * A308452 A308453 A308454 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 27 2019 STATUS approved

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Last modified February 5 12:36 EST 2023. Contains 360084 sequences. (Running on oeis4.)