A308120 Take all the integer-sided triangles with perimeter n and prime sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's.

0, 0, 0, 0, 0, 2, 2, 3, 3, 0, 3, 5, 5, 0, 10, 7, 12, 0, 7, 0, 7, 0, 7, 11, 18, 0, 29, 13, 35, 0, 24, 0, 24, 0, 35, 17, 43, 0, 71, 19, 77, 0, 62, 0, 49, 0, 83, 23, 91, 0, 76, 0, 76, 0, 38, 0, 59, 0, 101, 29, 67, 0, 140, 31, 194, 0, 121, 0, 125, 0, 104, 0, 83

Offset

1,6

Links

Table of n, a(n) for n=1..73.

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

Mathematica

Table[Sum[Sum[i (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. A308109.

Sequence in context: A164089 A300290 A068460 * A143797 A319772 A079729

Adjacent sequences: A308117 A308118 A308119 * A308121 A308122 A308123

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved