A306464 Sum of the largest side lengths of all integer-sided triangles with perimeter n whose largest side length is prime.

0, 0, 0, 0, 2, 2, 6, 3, 3, 0, 15, 10, 10, 5, 33, 21, 21, 14, 14, 7, 7, 0, 66, 55, 55, 44, 135, 111, 111, 87, 87, 63, 63, 39, 192, 162, 162, 132, 322, 273, 273, 237, 237, 201, 201, 165, 441, 382, 382, 323, 323, 264, 264, 222, 222, 180, 180, 138, 573, 521, 521

Offset

1,5

Links

Table of n, a(n) for n=1..61.

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(n-i-k) * (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - k) (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. A010051, A306426.

Sequence in context: A344007 A130478 A308140 * A338449 A163890 A298983

Adjacent sequences: A306461 A306462 A306463 * A306465 A306466 A306467

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 03 2019

Status

approved