A308451 Number of integer-sided triangles with perimeter n whose largest side length is prime.

0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 3, 2, 2, 1, 5, 3, 3, 2, 2, 1, 1, 0, 6, 5, 5, 4, 11, 9, 9, 7, 7, 5, 5, 3, 12, 10, 10, 8, 18, 15, 15, 13, 13, 11, 11, 9, 21, 18, 18, 15, 15, 12, 12, 10, 10, 8, 8, 6, 21, 19, 19, 17, 33, 30, 30, 27, 27, 24, 24, 21, 21, 19, 19, 17

Offset

1,7

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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))) * c(n-i-k), where c(n) is the prime characteristic (A010051).

Maple

f:= proc(n) local p, v;
  v:= add(1/2*(3*p-n+1)+`if`((n-p)::even, 1/2, 0), p = select(isprime, [$ceil(n/3)..floor((n-1)/2)]));
end proc:
map(f, [$1..100]); # Robert Israel, May 28 2019

Mathematica

Table[Sum[Sum[ (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, A308450.

Sequence in context: A334204 A336362 A336363 * A308067 A124748 A161225

Adjacent sequences: A308448 A308449 A308450 * A308452 A308453 A308454

Keyword

nonn

Author

Wesley Ivan Hurt, May 27 2019

Status

approved