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a(n) = A184220(n)/A133150(n) unless A133150(n) = 0 in which case a(n) = 0.
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%I #7 Mar 30 2012 17:25:56

%S 0,0,0,0,1,1,2,1,2,1,2,1,2,1,2,1,2,7,7,1,2,1,2,1,7,7,2,1,2,1,2,7,14,1,

%T 2,1,2,1,14,7,17,1,2,1,2,17,14,1,2,1,2,23,14,7,2,1,2,17,2,7,14,1,17,1,

%U 23,1,14,7,2,1,31,1,2,7,34,1,2,1

%N a(n) = A184220(n)/A133150(n) unless A133150(n) = 0 in which case a(n) = 0.

%C a(n) is the "level" of squares (A000290).

%C The decomposition of squares into weight * level + gap is A000217(n) = A133150(n) * a(n) + A005408(n) if a(n) > 0.

%C A184220(n) = A000290(n) - A005408(n) if A000217(n) - A005408(n) > A005408(n), 0 otherwise.

%H Rémi Eismann, <a href="/A184221/b184221.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 3 we have A133150(3) = 0, hence a(3) = 0.

%e For n = 5 we have A184220(5)/A133150(5) = 14 / 14 = 1, hence a(5) = 1.

%e For n = 25 we have A184220(25)/A133150(25) = 574 / 82 = 5, hence a(25) = 7.

%Y Cf. A000290, A005408, A133150, A184220, A118534, A117078, A117563, A001223.

%K nonn

%O 1,7

%A _Rémi Eismann_, Jan 10 2011