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A306464
Sum of the largest side lengths of all integer-sided triangles with perimeter n whose largest side length is prime.
0
0, 0, 0, 0, 2, 2, 6, 3, 3, 0, 15, 10, 10, 5, 33, 21, 21, 14, 14, 7, 7, 0, 66, 55, 55, 44, 135, 111, 111, 87, 87, 63, 63, 39, 192, 162, 162, 132, 322, 273, 273, 237, 237, 201, 201, 165, 441, 382, 382, 323, 323, 264, 264, 222, 222, 180, 180, 138, 573, 521, 521
OFFSET
1,5
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) * (n-i-k).
MATHEMATICA
Table[Sum[Sum[(n - i - k) (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
Sequence in context: A344007 A130478 A308140 * A338449 A163890 A298983
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 03 2019
STATUS
approved