A073068 Minimum value of abs(n-x*tau(x)) x>0.
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, 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, 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
Offset: 1
Keywords
Programs
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PARI
a(n)=vecmin(vector(n,k,abs(n-k*numdiv(k))))
Formula
a(A036438(n))=0 . It seems that sum(k=1, n, a(k)) is asymptotic to C*n with 1.5