OFFSET
1,6
LINKS
Eric Weisstein's World of Mathematics, Moebius Function
FORMULA
G.f.: (1/(1 - x)) * (x - Sum_{k>=2} mu(k-1) * x^k / (1 - x^k)).
a(n) = 1 - Sum_{k=1..n} Sum_{d|k, d > 1} mu(d-1) for n > 0.
Sum_{k=1..n-1} mu(k) * a(floor(n/k)) = 0.
MATHEMATICA
Table[Sum[MoebiusMu[Floor[n/k]], {k, 1, n}], {n, 1, 85}]
Table[1 - Sum[DivisorSum[k, MoebiusMu[# - 1] &, # > 1 &], {k, 1, n}], {n, 1, 85}]
nmax = 85; CoefficientList[Series[(1/(1 - x)) (x - Sum[MoebiusMu[k - 1] x^k/(1 - x^k), {k, 2, nmax}]), {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sum(k=1, n, moebius(n\k)); \\ Michel Marcus, Feb 14 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 14 2020
STATUS
approved