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A308257 Take all the integer-sided triangles with perimeter n and nonprime sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's. 0
0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 6, 4, 0, 6, 8, 12, 15, 14, 24, 31, 17, 35, 38, 45, 27, 49, 42, 71, 64, 76, 92, 118, 73, 117, 110, 149, 97, 146, 121, 194, 170, 217, 240, 294, 184, 277, 249, 339, 349, 389, 381, 502, 514, 566, 618, 693, 538, 658, 672, 764 (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) * i.

MATHEMATICA

Table[Sum[Sum[i*(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.

Sequence in context: A204301 A204084 A096904 * A308256 A096406 A189885

Adjacent sequences:  A308254 A308255 A308256 * A308258 A308259 A308260

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 17 2019

STATUS

approved

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)