OFFSET
1,1
COMMENTS
a(720) = -1 is the first negative term.
LINKS
FORMULA
MATHEMATICA
f[p_, e_] := e*2^(PrimePi[p] - 1); s[1] = 1; s[n_] := Boole@Divisible[Plus @@ f @@@ FactorInteger[n], 3]; sinv[1] = 1; sinv[n_] := -DivisorSum[n, sinv[#]*s[n/#] &, # < n &]; a[n_] := s[n] + sinv[n]; Array[a, 100] (* Amiram Eldar, Apr 15 2022 *)
PROG
(PARI)
up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
v353348 = DirInverseCorrect(vector(up_to, n, A353350(n)));
A353348(n) = v353348[n];
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Apr 15 2022
STATUS
approved