A308256 Sum of the largest side lengths of all integer-sided triangles with perimeter n and nonprime sides.

0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 6, 6, 0, 6, 8, 14, 18, 16, 28, 37, 19, 37, 43, 53, 31, 56, 50, 88, 86, 95, 118, 148, 91, 134, 130, 178, 113, 165, 143, 231, 212, 263, 299, 361, 224, 323, 304, 409, 431, 471, 475, 612, 646, 684, 764, 840, 644, 767, 802, 909

Offset

1,9

Links

Table of n, a(n) for n=1..62.

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) * (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - 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: A204084 A096904 A308257 * A096406 A189885 A151673

Adjacent sequences: A308253 A308254 A308255 * A308257 A308258 A308259

Keyword

nonn

Author

Wesley Ivan Hurt, May 17 2019

Status

approved