OFFSET
1,3
COMMENTS
Moebius transform of quarter-squares (A002620).
FORMULA
G.f.: Sum_{k>=1} mu(k) * x^(2*k) / ((1 + x^k) * (1 - x^k)^3).
a(n) = J_2(n) / 4 for n >= 3, where J_() is the Jordan function.
MATHEMATICA
Table[Sum[MoebiusMu[n/d] Floor[d^2/4], {d, Divisors[n]}], {n, 1, 61}]
nmax = 61; CoefficientList[Series[Sum[MoebiusMu[k] x^(2 k)/((1 + x^k) (1 - x^k)^3), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(d^2\4)); \\ Michel Marcus, Aug 03 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved