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A308307
Number of integer-sided triangles with perimeter n and at least one side length that is not semiprime.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 19 2019
STATUS
approved