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%I #14 Feb 26 2024 10:42:35
%S 1,0,1,1,3,0,5,0,4,0,9,-1,11,0,-1,2,15,0,17,-1,-1,0,21,0,16,0,12,-1,
%T 27,0,29,4,-1,0,3,0,35,0,-1,0,39,0,41,-1,4,0,45,0,36,0,-1,-1,51,0,7,0,
%U -1,0,57,1,59,0,-4,8,-3,0,65,-1,-1,0
%N Möbius transform of reduced totient function (A002322).
%C Since A002322(n) = A000010(n) for n = 1, 2, 4, and odd prime powers, a(n) = A007431(n) for the same values of n.
%F a(n) = Sum_{d|n} A008683(d) * A002322(n/d).
%e a(8) = mu(1)*lambda(8) + mu(2)*lambda(4) + mu(4)*lambda(2) + mu(8)*lambda(1) = 0.
%t a[n_] := DivisorSum[n, MoebiusMu[#] * CarmichaelLambda[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Jan 29 2024 *)
%o (PARI) a(n) = sumdiv(n, d, moebius(d)*lcm(znstar(n/d)[2]))
%Y Cf. A008683, A002322, A000010, A007431.
%K sign
%O 1,5
%A _Miles Englezou_, Jan 29 2024
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