A308253 Number of integer-sided triangles with perimeter n and nonprime side lengths.

0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 3, 4, 2, 4, 4, 5, 3, 5, 4, 7, 6, 7, 8, 10, 6, 9, 8, 11, 7, 10, 8, 13, 11, 14, 15, 18, 11, 16, 14, 19, 19, 21, 20, 26, 26, 28, 30, 33, 25, 30, 30, 34, 27, 32, 29, 37, 35, 39, 40, 45, 44, 47, 47, 53

Offset

1,18

Links

Table of n, a(n) for n=1..74.

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))) * c(i) * c(k) * c(n-i-k), where c(n) = A005171(n).

Mathematica

Table[Sum[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - 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. A005171.

Sequence in context: A052275 A338139 A244798 * A286614 A359481 A023508

Adjacent sequences: A308250 A308251 A308252 * A308254 A308255 A308256

Keyword

nonn

Author

Wesley Ivan Hurt, May 17 2019

Status

approved