OFFSET
1,3
LINKS
FORMULA
a(n) = (n/2) * Sum_{i=1..floor(n/2)} i * (n-i) * mu(i)^2 * mu(n-i)^2, where mu is the Möbius function (A008683).
MAPLE
N:= 100: # for a(1)..a(N)
A:= Vector(N):
SF:= select(numtheory:-issqrfree, [$1..N-1]):
for iq from 1 to nops(SF) do
q:= SF[iq];
for ip from 1 to iq do
p:= SF[ip];
n:= p+q;
if n > N then break fi;
A[n]:= A[n] + p*q*(p+q)/2
od
od:
convert(A, list); # Robert Israel, Jun 12 2018
MATHEMATICA
Table[(n/2)*Sum[i (n - i)*MoebiusMu[i]^2 MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 80}]
PROG
(Magma) [0] cat [&+[k*(n-k)*(MoebiusMu(k)^2*MoebiusMu(n-k)^2)*n/2: k in [1..Floor(n/2)]]: n in [2..60]]; // Vincenzo Librandi, Apr 21 2018
(PARI) a(n) = n*sum(i=1, n\2, i*(n-i)*moebius(i)^2*moebius(n-i)^2)/2; \\ Michel Marcus, Apr 21 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 19 2018
STATUS
approved