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A349446
a(n) = A349444(n) + A349445(n).
4
2, 0, 0, 1, 0, -2, 0, 1, 1, -4, 0, -1, 0, -6, 4, 1, 0, -5, 0, -2, 6, -10, 0, -1, 4, -12, 5, -3, 0, -4, 0, 1, 10, -16, 12, -2, 0, -18, 12, -2, 0, -6, 0, -5, 14, -22, 0, -1, 9, -16, 16, -6, 0, -13, 20, -3, 18, -28, 0, 0, 0, -30, 21, 1, 24, -10, 0, -8, 22, -12, 0, -2, 0, -36, 24, -9, 30, -12, 0, -2, 19, -40, 0, 0, 32
OFFSET
1,1
LINKS
FORMULA
a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A349444(d) * A349445(n/d). [As the sequences are Dirichlet inverses of each other]
MATHEMATICA
s[n_] := MoebiusMu[n] - If[OddQ[n], 0, MoebiusMu[n/2]]; k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; kinv[1] = 1; kinv[n_] := kinv[n] = -DivisorSum[n, kinv[#]*k[n/#] &, # < n &]; a[n_] := DivisorSum[n, s[#]*k[n/#] + IntegerExponent[2*#, 2]*kinv[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2021 *)
PROG
(PARI) A349446(n) = (A349444(n)+A349445(n)); \\ Needs also code from A349444 and A349445.
CROSSREFS
Cf. also A349433.
Sequence in context: A353367 A349439 A323882 * A353469 A349433 A346478
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 18 2021
STATUS
approved