A308254 - OEIS

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A308254

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

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: A095269 A356302 A308275 * A111417 A007271 A327449

Adjacent sequences: A308251 A308252 A308253 * A308255 A308256 A308257

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 17 2019

STATUS

approved