

A335621


Number of integersided triangles with perimeter n such that the sum of each pair of side lengths is squarefree.


1



0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 1, 2, 3, 4, 2, 3, 2, 2, 4, 5, 4, 4, 3, 3, 3, 3, 5, 5, 4, 4, 6, 8, 5, 8, 8, 12, 7, 12, 7, 10, 6, 10, 10, 15, 14, 20, 14, 18, 17, 21, 20, 25, 20, 23, 18, 19, 16, 20, 22, 24, 21, 25, 21, 22, 20, 22, 23, 28, 22, 28, 22, 24, 20, 23, 25
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,9


LINKS



FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((nk)/2} sign(floor((i+k)/(nik+1))) * mu(i+k)^2 * mu(ni)^2 * mu(nk)^2, where mu is the Möbius function (A008683).


MATHEMATICA

Table[Sum[Sum[MoebiusMu[i + k]^2*MoebiusMu[n  i]^2*MoebiusMu[n  k]^2 * Sign[Floor[(i + k)/(n  i  k + 1)]], {i, k, Floor[(n  k)/2]}], {k, Floor[n/3]}], {n, 100}]


CROSSREFS

Cf. A335621 (averages of each pair of side lengths is prime).


KEYWORD

nonn


AUTHOR



STATUS

approved



