A308100 Sum of the largest sides of all integer-sided triangles with prime sides and perimeter n.

0, 0, 0, 0, 0, 2, 3, 3, 3, 0, 5, 5, 5, 0, 12, 7, 14, 0, 7, 0, 7, 0, 11, 11, 22, 0, 37, 13, 37, 0, 26, 0, 24, 0, 47, 17, 47, 0, 85, 19, 91, 0, 74, 0, 55, 0, 105, 23, 107, 0, 82, 0, 88, 0, 42, 0, 65, 0, 133, 29, 81, 0, 172, 31, 234, 0, 153, 0, 143, 0, 120, 0

Offset: 1

Author

Wesley Ivan Hurt, May 13 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A308119.

Programs

Mathematica

Table[Sum[Sum[(n - i - k) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[k] - PrimePi[k - 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}]

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