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A349568
Dirichlet convolution of A011782 [2^(n-1)] with A349453 (Dirichlet inverse of A133494, 3^(n-1)).
5
1, -1, -5, -16, -65, -187, -665, -1984, -6260, -18895, -58025, -174016, -527345, -1583407, -4765595, -14307568, -42981185, -128980852, -387158345, -1161657760, -3485726195, -10458022927, -31376865305, -94134053296, -282412754000, -847252941535, -2541798630320, -7625456893096, -22876524019505, -68629821114805
OFFSET
1,3
COMMENTS
Dirichlet convolution of this sequence with A034754 produces A034738.
LINKS
FORMULA
a(n) = Sum_{d|n} 2^(d-1) * A349453(n/d).
MATHEMATICA
s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 3^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, 2^(# - 1) * s[n/#] &]; Array[a, 30] (* Amiram Eldar, Nov 22 2021 *)
PROG
(PARI)
A133494(n) = max(1, 3^(n-1));
memoA349453 = Map();
A349453(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349453, n, &v), v, v = -sumdiv(n, d, if(d<n, A133494(n/d)*A349453(d), 0)); mapput(memoA349453, n, v); (v)));
A349568(n) = sumdiv(n, d, (2^(d-1)) * A349453(n/d));
CROSSREFS
Cf. A011782, A133494, A349453, A349567 (Dirichlet inverse).
Sequence in context: A092497 A275100 A301958 * A026525 A007043 A128242
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 22 2021
STATUS
approved