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A308256 Sum of the largest side lengths of all integer-sided triangles with perimeter n and nonprime sides. 0
0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 6, 6, 0, 6, 8, 14, 18, 16, 28, 37, 19, 37, 43, 53, 31, 56, 50, 88, 86, 95, 118, 148, 91, 134, 130, 178, 113, 165, 143, 231, 212, 263, 299, 361, 224, 323, 304, 409, 431, 471, 475, 612, 646, 684, 764, 840, 644, 767, 802, 909 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..62.

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))) * A005171(i) * A005171(k) * A005171(n-i-k) * (n-i-k).

MATHEMATICA

Table[Sum[Sum[(n - i - k)*(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: A204084 A096904 A308257 * A096406 A189885 A151673

Adjacent sequences:  A308253 A308254 A308255 * A308257 A308258 A308259

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 17 2019

STATUS

approved

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Last modified January 28 01:00 EST 2022. Contains 350654 sequences. (Running on oeis4.)