login
A308512
Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose smallest side length is prime.
0
0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 8, 5, 8, 5, 13, 10, 18, 15, 23, 15, 30, 22, 37, 29, 44, 36, 51, 36, 51, 36, 51, 36, 62, 47, 73, 58, 84, 69, 108, 93, 132, 117, 156, 130, 169, 143, 182, 156, 195, 169, 225, 186, 242, 203, 259, 220, 295, 256, 331, 292, 367, 328
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(k) * k.
MATHEMATICA
Table[Sum[Sum[k (PrimePi[k] - PrimePi[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: A163946 A240500 A344264 * A308857 A244480 A308923
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 02 2019
STATUS
approved