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%I #6 Mar 31 2012 14:42:50
%S 0,4,7,2,4,5,13,2,7,4,19,2,4,23,2,5,2,13,4,31,2,3,2,17,37,2,19,4,43,2,
%T 4,47,2,7,2,5,53,2,5,2,4,29,61,2,3,2,4,67,2,4,5,73,2,3,2,4,79,2,4,83,
%U 2,5,2,43,89,2,7,2,3,2,47,97
%N a(n) = smallest k such that A002808(n+1) = A002808(n) + (A002808(n) mod k), or 0 if no such k exists.
%C a(n) is the "weight" of composite numbers.
%C The decomposition of composite numbers into weight * level + gap is A002808(n) = a(n) * A179621(n) + A073783(n) if a(n) > 0.
%H Remi Eismann, <a href="/A130882/b130882.txt">Table of n, a(n) for n=1..9999</a>
%e For n = 1 we have A002808(n) = 4, A002808(n+1) = 6; there is no k such that 6 - 4 = 2 = (4 mod k), hence a(1) = 0.
%e For n = 3 we have A002808(n) = 8, A002808(n+1) = 9; 7 is the smallest k such that 9 - 8 = 1 = (8 mod k), hence a(3) = 7.
%e For n = 24 we have A002808(n) = 36, A002808(n+1) = 38; 17 is the smallest k such that 38 - 36 = 2 = (36 mod k), hence a(24) = 17.
%Y Cf. A020639, A117078, A117563, A001223, A118534, A090369, A090368, A130533, A130650, A130703.
%K nonn
%O 1,2
%A _Rémi Eismann_, Aug 21 2007 - Jan 09 2011
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