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A349447
Dirichlet convolution of A003602 (Kimberling's paraphrases) with A326937 (Dirichlet inverse of A000265).
11
1, 0, -1, 0, -2, 0, -3, 0, -1, 0, -5, 0, -6, 0, 4, 0, -8, 0, -9, 0, 6, 0, -11, 0, -2, 0, -1, 0, -14, 0, -15, 0, 10, 0, 12, 0, -18, 0, 12, 0, -20, 0, -21, 0, 4, 0, -23, 0, -3, 0, 16, 0, -26, 0, 20, 0, 18, 0, -29, 0, -30, 0, 6, 0, 24, 0, -33, 0, 22, 0, -35, 0, -36, 0, 4, 0, 30, 0, -39, 0, -1, 0, -41, 0, 32, 0, 28
OFFSET
1,5
COMMENTS
Dirichlet convolution of this sequence with A264740 is A349371.
LINKS
FORMULA
a(n) = Sum_{d|n} A003602(d) * A326937(n/d).
MATHEMATICA
k[n_] := (n/2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, MoebiusMu[#] * # / 2^IntegerExponent[#, 2] * k[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2021 *)
PROG
(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
A006519(n) = (1<<valuation(n, 2));
A055615(n) = (n*moebius(n));
A326937(n) = (A055615(n)/A006519(n));
A349447(n) = sumdiv(n, d, A003602(d)*A326937(n/d));
CROSSREFS
Cf. A000265, A003602, A326937, A349448 (Dirichlet inverse).
Sequence in context: A135523 A194663 A135685 * A164658 A079067 A356676
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 19 2021
STATUS
approved