A308119 Sum of the smallest side lengths of all integer-sided triangles with prime side lengths and perimeter n.

0, 0, 0, 0, 0, 2, 2, 2, 3, 0, 3, 2, 3, 0, 8, 2, 8, 0, 5, 0, 7, 0, 5, 2, 10, 0, 15, 2, 15, 0, 12, 0, 18, 0, 23, 2, 21, 0, 39, 2, 37, 0, 36, 0, 31, 0, 47, 2, 47, 0, 46, 0, 48, 0, 30, 0, 47, 0, 61, 2, 35, 0, 66, 2, 92, 0, 61, 0, 77, 0, 60, 0, 43, 0, 79, 2, 90

Offset: 1

Author

Wesley Ivan Hurt, May 13 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A010051, A070088.

Programs

Mathematica

Table[Sum[Sum[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))) * c(i) * c(k) * c(n-i-k) * k, where c is the prime characteristic (A010051).