OFFSET
1,5
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))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2 * (n-i-k), where mu is the Möbius function (A008683).
MAPLE
N:= 100: # for a(1)..a(N)
SF:= select(numtheory:-issqrfree, [$1..N/2]):
V:= Vector(N):
for ia from 1 to nops(SF) do
a:= SF[ia];
if 2*a >= N then break fi;
for ib from ia by -1 to 1 do
b:= SF[ib];
if 2*b <= a then break fi;
cs:= select(c -> b+c > a, SF[1...ib]);
P:= select(`<=`, map(c -> a+b+c, cs), N);
V[P]:= V[P] +~ a;
od od:
convert(V, list); # Robert Israel, May 14 2019
MATHEMATICA
Table[Sum[Sum[(n - i - k)* MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - i]^2 *Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
PROG
(PARI) a(n) = sum(k=1, n\3, sum(i=k, (n-k)\2, sign((i+k)\(n-i-k+1))* issquarefree(i)*issquarefree(k)*issquarefree(n-i-k)*(n-i-k))); \\ Michel Marcus, May 14 2019
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Wesley Ivan Hurt, May 14 2019
STATUS
approved