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%I #18 May 18 2020 18:46:32
%S 1,1,3,3,5,3,6,5,6,5,15,5,9,6,10,10,20,6,21,10,9,15,36,10,25,9,21,9,
%T 41,10,30,20,25,20,18,9,33,21,18,20,50,9,51,25,18,36,72,20,51,25,40,
%U 18,65,21,50,18,33,41,87,20,45,30,33,40,36,25,75,40,61,18,120,18,66,33,50,33
%N a(n) = sum_{d | phi(n)} mu( phi(d) ) * phi(n)/d, where phi = A000010.
%C Fixed points are in A074701.
%H Antti Karttunen, <a href="/A163167/b163167.txt">Table of n, a(n) for n = 1..10001</a>
%F a(n) = A289627(A000010(n)). - _Antti Karttunen_, Jul 17 2017
%p with(numtheory):
%p A163167:=proc(n)
%p local div:
%p div:=convert(divisors(phi(n)), list):
%p add( mobius(phi(d))*phi(n)/d, d=div) ;
%p end proc:
%p seq(A163167(n),n=1..120) ;
%t Table[Sum[MoebiusMu[EulerPhi[d]] EulerPhi[n]/d, {d, Divisors[EulerPhi[n]]}], {n, 100}] (* _Indranil Ghosh_, Jul 17 2017 *)
%o (PARI) A163167(n) = sumdiv(eulerphi(n),d, moebius(eulerphi(d))*eulerphi(n)/d); \\ _Antti Karttunen_, Jul 17 2017
%o (PARI)
%o A289627(n) = sumdiv(n,d, moebius(eulerphi(d))*n/d);
%o A163167(n) = A289627(eulerphi(n)); \\ _Antti Karttunen_, Jul 17 2017
%o (Python)
%o from sympy import mobius, totient, divisors
%o def a(n):
%o tn = totient(n)
%o return sum(mobius(totient(d))*tn//d for d in divisors(tn))
%o print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Jul 17 2017
%Y Cf. A000010, A008683, A074701, A289627.
%K easy,nonn
%O 1,3
%A _R. J. Mathar_, Jul 22 2009
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