A308307 Number of integer-sided triangles with perimeter n and at least one side length that is not semiprime.

0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 3, 7, 4, 8, 6, 9, 8, 11, 8, 13, 10, 15, 13, 18, 15, 19, 17, 23, 19, 24, 20, 28, 26, 32, 28, 35, 32, 40, 36, 43, 38, 44, 40, 50, 46, 54, 49, 57, 52, 60, 56, 66, 58, 69, 66, 78, 72, 80, 76, 89, 83, 93, 88, 99, 91, 100, 96

Offset

1,7

Links

Table of n, a(n) for n=1..70.

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))) * (1 - A064911(i) * A064911(k) * A064911(n-i-k)).

a(n) = A005044(n) - A308069(n).

Mathematica

Table[Sum[Sum[(1 - 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. A005044, A064911, A308069.

Sequence in context: A290636 A106466 A130722 * A147541 A308308 A024162

Adjacent sequences: A308304 A308305 A308306 * A308308 A308309 A308310

Keyword

nonn

Author

Wesley Ivan Hurt, May 19 2019

Status

approved