A308450 Number of integer-sided triangles with perimeter n whose smallest side length is prime.

0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 4, 7, 5, 8, 6, 9, 7, 10, 7, 10, 7, 10, 7, 11, 8, 12, 9, 13, 10, 15, 12, 17, 14, 19, 15, 20, 16, 21, 17, 22, 18, 24, 19, 25, 20, 26, 21, 28, 23, 30, 25, 32, 27, 34, 29, 36, 31, 38, 32, 40, 34, 42, 36

Offset

1,9

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * c(k), where c(n) is the prime characteristic (A010051).

Mathematica

Table[Sum[Sum[ (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.

Sequence in context: A060129 A327161 A350067 * A229123 A173908 A329045

Adjacent sequences: A308447 A308448 A308449 * A308451 A308452 A308453

Keyword

nonn

Author

Wesley Ivan Hurt, May 27 2019

Status

approved