A308515 Take all the integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c and c is prime. a(n) is the sum of all the b's.

0, 0, 0, 0, 2, 2, 5, 3, 3, 0, 12, 9, 9, 5, 27, 18, 18, 13, 13, 7, 7, 0, 51, 45, 45, 38, 108, 93, 93, 76, 76, 57, 57, 36, 153, 133, 133, 111, 256, 222, 222, 199, 199, 174, 174, 147, 357, 316, 316, 272, 272, 225, 225, 193, 193, 159, 159, 123, 453, 420, 420

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) * i.

Mathematica

Table[Sum[Sum[i (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: A258803 A157495 A308143 * A361328 A128134 A157223

Adjacent sequences: A308512 A308513 A308514 * A308516 A308517 A308518

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 03 2019

Status

approved