A308069 Number of integer-sided triangles with perimeter n whose side lengths are semiprime.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 3, 4, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 4, 4, 2, 2, 2, 3, 4, 4, 5, 5, 4, 7, 6, 4, 2, 3, 5, 4, 2, 2, 3, 3, 3, 5, 8, 6, 6, 7, 7, 8, 7, 7, 10, 9, 9, 10, 12, 14, 10, 7, 9

Offset

1,22

Links

Table of n, a(n) for n=1..85.

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))) * c(i) * c(k) * c(n-i-k), where c is the semiprime characteristic (A064911).

Mathematica

Table[Sum[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[k], 2] KroneckerDelta[PrimeOmega[n - i - k], 2]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Cf. A064911.

Sequence in context: A337277 A269974 A269975 * A161895 A048138 A165022

Adjacent sequences: A308066 A308067 A308068 * A308070 A308071 A308072

Keyword

nonn

Author

Wesley Ivan Hurt, May 10 2019

Status

approved