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 A353349 Sum of A353350 and its Dirichlet inverse. 4
 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(720) = -1 is the first negative term. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A353348(n) + A353350(n). a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1= 1. 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

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Last modified December 6 16:00 EST 2022. Contains 358644 sequences. (Running on oeis4.)