A308100 Sum of the largest sides of all integer-sided triangles with prime sides and perimeter n.

0, 0, 0, 0, 0, 2, 3, 3, 3, 0, 5, 5, 5, 0, 12, 7, 14, 0, 7, 0, 7, 0, 11, 11, 22, 0, 37, 13, 37, 0, 26, 0, 24, 0, 47, 17, 47, 0, 85, 19, 91, 0, 74, 0, 55, 0, 105, 23, 107, 0, 82, 0, 88, 0, 42, 0, 65, 0, 133, 29, 81, 0, 172, 31, 234, 0, 153, 0, 143, 0, 120, 0

Offset

1,6

Links

Table of n, a(n) for n=1..72.

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) * (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - 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. A308119.

Sequence in context: A351188 A153878 A118925 * A351065 A171576 A016738

Adjacent sequences: A308097 A308098 A308099 * A308101 A308102 A308103

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved