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A306426
Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose largest side length is prime.
2
0, 0, 0, 0, 1, 2, 3, 2, 3, 0, 6, 5, 7, 4, 15, 9, 12, 9, 11, 6, 7, 0, 21, 20, 25, 22, 54, 48, 57, 47, 54, 40, 45, 27, 75, 65, 75, 61, 124, 105, 120, 110, 123, 109, 120, 102, 189, 166, 184, 155, 170, 135, 147, 125, 135, 109, 117, 87, 213, 199, 218, 200, 353
OFFSET
1,6
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) * k.
MATHEMATICA
Table[Sum[Sum[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: A059905 A295301 A308133 * A014836 A197262 A085032
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 03 2019
STATUS
approved