A308255 Sum of the smallest side lengths of all integer-sided triangles with perimeter n and nonprime sides.

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

Offset

1,12

Links

Table of n, a(n) for n=1..64.

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