A308318 Number of integer-sided triangles with perimeter n and at least one nonprime side length.

0, 0, 1, 0, 1, 0, 1, 0, 2, 2, 3, 2, 4, 4, 5, 4, 6, 7, 9, 8, 11, 10, 13, 11, 14, 14, 16, 15, 18, 19, 22, 21, 25, 24, 27, 26, 30, 30, 32, 32, 35, 37, 40, 40, 45, 44, 47, 47, 51, 52, 57, 56, 61, 61, 68, 65, 72, 70, 75, 74, 82, 80, 85, 84, 88, 91, 97, 96, 103

Offset

1,9

Links

Table of n, a(n) for n=1..69.

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

a(n) = A005044(n) - A070088(n).

Mathematica

Table[Sum[Sum[(1 - (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. A005044, A010051, A070088.

Sequence in context: A233777 A048620 A291271 * A165419 A117660 A358015

Adjacent sequences: A308315 A308316 A308317 * A308319 A308320 A308321

Keyword

nonn

Author

Wesley Ivan Hurt, May 19 2019

Status

approved