A308514 Take all the integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c and a is prime. a(n) is the sum of all the b's.

0, 0, 0, 0, 0, 2, 2, 3, 6, 7, 11, 9, 14, 11, 22, 18, 31, 26, 41, 30, 54, 41, 68, 53, 83, 66, 99, 73, 109, 80, 119, 87, 140, 105, 162, 124, 185, 144, 222, 178, 261, 214, 302, 241, 334, 269, 367, 298, 401, 328, 453, 363, 494, 399, 536, 436, 598, 493, 662, 552

Offset

1,6

Links

Table of n, a(n) for n=1..60.

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) * i.

Mathematica

Table[Sum[Sum[i (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}]
Table[Total[Select[IntegerPartitions[n, {3}], PrimeQ[#[[3]]]&&#[[3]]+#[[2]]>#[[1]]&][[All, 2]]], {n, 100}] (* Harvey P. Dale, Nov 27 2020 *)

Crossrefs

Cf. A010051, A308450, A308513.

Sequence in context: A091770 A032058 A241744 * A039866 A106369 A298436

Adjacent sequences: A308511 A308512 A308513 * A308515 A308516 A308517

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 02 2019

Status

approved