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%I #5 Mar 30 2012 17:25:56
%S 0,0,0,2,5,4,3,3,2,13,13,3,17,2,3,4,23,2,29,29,2,3,3,2,37,37,2,41,4,3,
%T 43,7,3,53,2,3,3,2,59,2,5,5,2,3,3,2,71,2,7,4,3,3,2,5,5,3,89,2,3,3,31,
%U 2,101,101,2,3,3,2,109,109,2,113,4,3,4,11,7,5,2,3,3,2
%N a(n) = smallest k such that A005117(n+1) = A005117(n) + (A005117(n) mod k), or 0 if no such k exists.
%C a(n) is the "weight" of squarefree numbers.
%C The decomposition of squarefree numbers into weight * level + gap is A005117(n) = a(n) * A184834(n) + A076259(n) if a(n) > 0.
%H Rémi Eismann, <a href="/A184832/b184832.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 1 we have A005117(1) = 1, A005117(2) = 2; there is no k such that 2 - 1 = 1 = (1 mod k), hence a(1) = 0.
%e For n = 4 we have A005117(4) = 5, A005117(5) = 6; 2 is the smallest k such that 6 - 5 = 1 = (5 mod k), hence a(4) = 2.
%e For n = 23 we have A005117(23) = 35, A005117(24) = 37; 3 is the smallest k such that 37 - 35 = 2 = (35 mod k), hence a(23) = 3.
%Y Cf. A005117, A076259, A184834, A184833, A117078, A117563, A001223, A118534.
%K nonn
%O 1,4
%A _Rémi Eismann_, Jan 23 2011
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