A306426 Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose largest side length is prime.

0, 0, 0, 0, 1, 2, 3, 2, 3, 0, 6, 5, 7, 4, 15, 9, 12, 9, 11, 6, 7, 0, 21, 20, 25, 22, 54, 48, 57, 47, 54, 40, 45, 27, 75, 65, 75, 61, 124, 105, 120, 110, 123, 109, 120, 102, 189, 166, 184, 155, 170, 135, 147, 125, 135, 109, 117, 87, 213, 199, 218, 200, 353

Offset

1,6

Links

Table of n, a(n) for n=1..63.

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

Mathematica

Table[Sum[Sum[k (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, A308451.

Sequence in context: A059905 A295301 A308133 * A014836 A197262 A085032

Adjacent sequences: A306423 A306424 A306425 * A306427 A306428 A306429

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 03 2019

Status

approved