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A308515 Take all the integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c and c is prime. a(n) is the sum of all the b's. 0
0, 0, 0, 0, 2, 2, 5, 3, 3, 0, 12, 9, 9, 5, 27, 18, 18, 13, 13, 7, 7, 0, 51, 45, 45, 38, 108, 93, 93, 76, 76, 57, 57, 36, 153, 133, 133, 111, 256, 222, 222, 199, 199, 174, 174, 147, 357, 316, 316, 272, 272, 225, 225, 193, 193, 159, 159, 123, 453, 420, 420 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..61.

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+1))) * A010051(n-i-k) * i.

MATHEMATICA

Table[Sum[Sum[i (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. A010051, A306426.

Sequence in context: A258803 A157495 A308143 * A128134 A157223 A174608

Adjacent sequences:  A308512 A308513 A308514 * A308516 A308517 A308518

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 03 2019

STATUS

approved

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Last modified August 11 05:42 EDT 2020. Contains 336422 sequences. (Running on oeis4.)