A308512 Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose smallest side length is prime.

0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 8, 5, 8, 5, 13, 10, 18, 15, 23, 15, 30, 22, 37, 29, 44, 36, 51, 36, 51, 36, 51, 36, 62, 47, 73, 58, 84, 69, 108, 93, 132, 117, 156, 130, 169, 143, 182, 156, 195, 169, 225, 186, 242, 203, 259, 220, 295, 256, 331, 292, 367, 328

Offset

1,6

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+1))) * A010051(k) * k.

Mathematica

Table[Sum[Sum[k (PrimePi[k] - PrimePi[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: A163946 A240500 A344264 * A308857 A244480 A308923

Adjacent sequences: A308509 A308510 A308511 * A308513 A308514 A308515

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 02 2019

Status

approved