OFFSET
1,2
COMMENTS
Dirichlet inverse of A003967.
Moebius transform of A097945.
From Vaclav Kotesovec, Feb 19 2021: (Start)
Abs(a(n)) <= n.
a(n) = n iff n is in A030229. (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{k=1..n} mu(gcd(n,k)) * mu(n/gcd(n,k)).
a(1) = 1; a(n) = -Sum_{d|n, d < n} A003967(n/d) * a(d).
a(n) = Sum_{d|n} mu(n/d) * A097945(d).
Multiplicative with a(p^e) = -p if e=1, p-1 if e=2, and 0 otherwise. - Amiram Eldar, Feb 19 2021
MATHEMATICA
Table[Sum[EulerPhi[d] MoebiusMu[d] MoebiusMu[n/d], {d, Divisors[n]}], {n, 65}]
Table[Sum[MoebiusMu[GCD[n, k]] MoebiusMu[n/GCD[n, k]], {k, n}], {n, 65}]
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*moebius(d)*moebius(n/d)); \\ Michel Marcus, Feb 17 2021
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, Feb 16 2021
STATUS
approved