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

1,6

Links

Table of n, a(n) for n=1..77.

Wikipedia, Integer Triangle

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).

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}]

Crossrefs

Cf. A010051, A070088.

Sequence in context: A305384 A112599 A347905 * A307299 A307298 A216674

Adjacent sequences: A308116 A308117 A308118 * A308120 A308121 A308122

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved