A308513 Sum of the largest side lengths of all integer-sided triangles with perimeter n whose smallest side length is prime.

0, 0, 0, 0, 0, 2, 3, 3, 7, 8, 14, 10, 17, 12, 25, 20, 36, 31, 50, 35, 63, 47, 79, 62, 98, 80, 120, 87, 130, 94, 140, 101, 161, 120, 185, 142, 212, 167, 255, 209, 304, 257, 359, 289, 397, 324, 438, 362, 482, 403, 546, 439, 589, 478, 635, 520, 703, 585, 777

Offset

1,6

Links

Table of n, a(n) for n=1..59.

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) * (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - 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: A062761 A375515 A117524 * A045683 A343031 A157531

Adjacent sequences: A308510 A308511 A308512 * A308514 A308515 A308516

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 02 2019

Status

approved