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A184833 a(n) = largest k such that A005117(n+1) = A005117(n) + (A005117(n) mod k), or 0 if no such k exists.

%I A184833 #5 Mar 30 2012 17:25:56
%S A184833 0,0,0,4,5,4,9,9,12,13,13,15,17,20,21,20,23,28,29,29,32,33,33,36,37,
%T A184833 37,40,41,40,45,43,49,51,53,56,57,57,60,59,64,65,65,68,69,69,72,71,76,
%U A184833 77,76,81,81,84,85,85,87,89,92,93,93,93,100,101,101,104,105
%N A184833 a(n) = largest k such that A005117(n+1) = A005117(n) + (A005117(n) mod k), or 0 if no such k exists.
%C A184833 From the definition, a(n) = A005117(n) - A076259(n) if A005117(n) - A076259(n) > A076259(n), 0 otherwise where A005117 are the squarefree numbers and A076259 are the gaps between squarefree numbers.
%H A184833 Rémi Eismann, <a href="/A184833/b184833.txt">Table of n, a(n) for n = 1..10000</a>
%e A184833 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 A184833 For n = 4 we have A005117(4) = 5, A005117(5) = 6; 4 is the largest k such that 6 - 5 = 1 = (5 mod k), hence a(4) = 2; a(3) = 5 - 1 = 4.
%e A184833 For n = 23 we have A005117(23) = 35, A005117(24) = 37; 33 is the largest k such that 37 - 35 = 2 = (35 mod k), hence a(23) = 33; a(24) = 35 - 2 = 33.
%Y A184833 Cf. A005117, A076259, A184832, A184834, A117078, A117563, A001223, A118534.
%K A184833 nonn,easy
%O A184833 1,4
%A A184833 _Rémi Eismann_, Jan 23 2011