A072612 - OEIS

%I #6 Mar 30 2012 18:39:04

%S 0,1,0,0,1,0,0,0,1,2,1,0,0,0,0,1,1,0,1,0,1,2,1,0,1,2,1,0,1,0,0,0,1,2,

%T 1,0,1,0,0,0,1,0,1,0,1,2,1,0,1,2,3,2,1,0,1,0,0,1,1,0,1,0,0,1,2,3,1,0,

%U 1,2,1,0,1,0,1,2,1,0,1,0,1,2,1,0,1,2,3,2,1,0,0,1,0,1,1,0,1,0,1,2,1,0,1,0,1

%N Minimal value of { abs(n-sigma(k)) : k>0 }.

%C a(A002191(k)) = 0

%F Conjecture : S(n) = sum( k=1, n, a(k) ) = n + O(sqrt(n)) and more precisely for n large enough : n - (5/2)*sqrt(n) < S(n) < n - (3/2)*sqrt(n)

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

%K easy,nonn

%O 1,10

%A _Benoit Cloitre_, Aug 11 2002