A308307 - OEIS

%I #7 Jun 18 2020 13:56:02

%S 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,

%T 23,19,24,20,28,26,32,28,35,32,40,36,43,38,44,40,50,46,54,49,57,52,60,

%U 56,66,58,69,66,78,72,80,76,89,83,93,88,99,91,100,96

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F 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)).

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

%t 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}]

%Y Cf. A005044, A064911, A308069.

%K nonn

%O 1,7

%A _Wesley Ivan Hurt_, May 19 2019