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A308254 Sum of the perimeters of all integer-sided triangles with perimeter n and nonprime side lengths. 0
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, 81, 140, 116, 210, 186, 224, 264, 340, 210, 324, 296, 418, 273, 400, 328, 546, 473, 616, 675, 828, 517, 768, 686, 950, 969, 1092, 1060, 1404, 1430, 1568, 1710, 1914 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..58.

Wikipedia, Integer Triangle

FORMULA

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).

MATHEMATICA

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}]

CROSSREFS

Cf. A005171, A308253.

Sequence in context: A123074 A095269 A308275 * A111417 A007271 A327449

Adjacent sequences:  A308251 A308252 A308253 * A308255 A308256 A308257

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 17 2019

STATUS

approved

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)