OFFSET
1,2
COMMENTS
Moebius transform applied twice to A076479 (unitary Moebius function).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Ilya Gutkovskiy, Scatter plot of partial sums of A326814 up to n=10000.
FORMULA
Multiplicative with a(p^e) = -3 if e = 1, 2 if e = 2, and 0 otherwise. - Amiram Eldar, Oct 26 2020
MATHEMATICA
Table[Sum[MoebiusMu[n/d] MoebiusMu[d] 2^PrimeNu[d], {d, Divisors[n]}], {n, 1, 75}]
f[p_, e_] := Which[e == 1, -3, e == 2, 2, e > 2, 0]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Oct 26 2020 *)
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*moebius(d)*2^omega(d)); \\ Michel Marcus, Oct 26 2020
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - 2*X)*(1 - X))[n], ", ")) \\ Vaclav Kotesovec, Aug 22 2021
CROSSREFS
KEYWORD
sign,mult,easy
AUTHOR
Ilya Gutkovskiy, Oct 19 2019
STATUS
approved