A308257 Take all the integer-sided triangles with perimeter n and nonprime sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's.

0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 6, 4, 0, 6, 8, 12, 15, 14, 24, 31, 17, 35, 38, 45, 27, 49, 42, 71, 64, 76, 92, 118, 73, 117, 110, 149, 97, 146, 121, 194, 170, 217, 240, 294, 184, 277, 249, 339, 349, 389, 381, 502, 514, 566, 618, 693, 538, 658, 672, 764

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) * i.

Mathematica

Table[Sum[Sum[i*(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.

Sequence in context: A204301 A204084 A096904 * A308256 A096406 A189885

Adjacent sequences: A308254 A308255 A308256 * A308258 A308259 A308260

Keyword

nonn

Author

Wesley Ivan Hurt, May 17 2019

Status

approved