A308165 Sum of the perimeters of all integer-sided triangles with perimeter n and prime sides.

0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 11, 12, 13, 0, 30, 16, 34, 0, 19, 0, 21, 0, 23, 24, 50, 0, 81, 28, 87, 0, 62, 0, 66, 0, 105, 36, 111, 0, 195, 40, 205, 0, 172, 0, 135, 0, 235, 48, 245, 0, 204, 0, 212, 0, 110, 0, 171, 0, 295, 60, 183, 0, 378, 64, 520, 0, 335, 0

Offset

1,6

Links

Table of n, a(n) for n=1..68.

Wikipedia, Integer Triangle

Formula

a(n) = n * A070088(n).

a(n) = 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).

Mathematica

Table[n*Sum[Sum[(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. A070088.

Sequence in context: A120207 A202703 A308147 * A090928 A199174 A335094

Adjacent sequences: A308162 A308163 A308164 * A308166 A308167 A308168

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved