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A308254 Sum of the perimeters of all integer-sided triangles with perimeter n and nonprime side lengths. 0

%I

%S 0,0,3,0,0,0,0,0,9,0,0,12,13,14,0,16,17,36,38,40,63,88,46,96,100,130,

%T 81,140,116,210,186,224,264,340,210,324,296,418,273,400,328,546,473,

%U 616,675,828,517,768,686,950,969,1092,1060,1404,1430,1568,1710,1914

%N Sum of the perimeters of all integer-sided triangles with perimeter n and nonprime side lengths.

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

%F a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k))) * A005171(i) * A005171(k) * A005171(n-i-k).

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

%Y Cf. A005171, A308253.

%K nonn

%O 1,3

%A _Wesley Ivan Hurt_, May 17 2019

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Last modified January 16 23:02 EST 2022. Contains 350376 sequences. (Running on oeis4.)