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a(n) = Sum_{d|n} mu(phi(d))*n/d.
2

%I #11 Aug 29 2023 04:19:41

%S 1,3,2,5,5,6,8,10,7,15,12,9,13,24,10,20,17,21,19,25,17,36,24,18,25,39,

%T 21,41,29,30,30,40,25,51,40,33,37,57,26,50,41,51,42,61,35,72,48,36,55,

%U 75,34,65,53,63,60,82,38,87,60,45,61,90,58,80,65,75,66,85,49,120,70,66,73,111,50,95,95,78,78,100,63,123,84,81

%N a(n) = Sum_{d|n} mu(phi(d))*n/d.

%H Antti Karttunen, <a href="/A289627/b289627.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{d|n} mu(phi(d))*n/d = Sum_{d|n} A008683(A000010(d))*n/d.

%F a(A000010(n)) = A163167(n).

%t a[n_] := DivisorSum[n, MoebiusMu[EulerPhi[#]] * n/# &]; Array[a, 100] (* _Amiram Eldar_, Aug 29 2023 *)

%o (PARI) A289627(n) = sumdiv(n,d, moebius(eulerphi(d))*n/d);

%Y Cf. A000010, A008683, A163167.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 17 2017