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Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose largest side length is prime.
2

%I #56 Jun 16 2020 13:40:42

%S 0,0,0,0,1,2,3,2,3,0,6,5,7,4,15,9,12,9,11,6,7,0,21,20,25,22,54,48,57,

%T 47,54,40,45,27,75,65,75,61,124,105,120,110,123,109,120,102,189,166,

%U 184,155,170,135,147,125,135,109,117,87,213,199,218,200,353

%N Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose largest side length is prime.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010051(n-i-k) * k.

%t Table[Sum[Sum[k (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}]

%Y Cf. A010051, A308451.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Jun 03 2019