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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)