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Minimum value of abs(n-x*tau(x)) x>0.
0

%I #6 Mar 30 2012 18:39:05

%S 0,1,1,0,1,0,1,2,1,0,1,0,1,0,1,2,3,4,3,2,1,0,1,0,1,0,0,1,2,2,1,0,1,0,

%T 1,2,1,0,1,0,1,2,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1,0,1,0,1,0,1,2,3,4,5,4,

%U 3,2,1,0,1,0,0,1,2,2,1,0,1,0,1,0,1,0,1,0,1,2,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1

%N Minimum value of abs(n-x*tau(x)) x>0.

%F a(A036438(n))=0 . It seems that sum(k=1, n, a(k)) is asymptotic to C*n with 1.5<C<2

%o (PARI) a(n)=vecmin(vector(n,k,abs(n-k*numdiv(k))))

%K nonn

%O 1,8

%A _Benoit Cloitre_, Aug 17 2002