The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A353348 Dirichlet inverse of A353350, where A353350 is the characteristic function for numbers k such that A048675(k) is a multiple of 3. 12
 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, -1, 0, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,120 COMMENTS From Antti Karttunen, Jan 17 2023: (Start) a(120) = 3 is the first term with absolute value larger than 1. As A353350 is not multiplicative, neither is this sequence. For all numbers n in A359830 (complement of A332820), a(n) = 0. Proof: In the convolution formula, when n is any term of A359830, at least the other of the divisors (n/d) and d is a term of A359830, because a product of any two terms of A332820 stays in A332820 (as it is a multiplicative semigroup), while a product of a term of A332820 and its complement A359830 is always in A359830. As A353350 is zero for all A359830, it is easy to see by induction that also a(n) is zero for all such numbers. Therefore, nonzero values (including any odd values, see A359827) occur only on a subset of A332820, and A359826(n) <= A353350(n). (End) LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(1) = 1; a(n) = -Sum_{d|n, d < n} A353350(n/d) * a(d). a(n) = A353349(n) - A353350(n). a(p) = 0 for all primes p. a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1. MATHEMATICA f[p_, e_] := e*2^(PrimePi[p] - 1); s[1] = 1; s[n_] := Boole @ Divisible[Plus @@ f @@@ FactorInteger[n], 3]; a[1] = 1; a[n_] := -DivisorSum[n, a[#]*s[n/#] &, # < 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)