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%I #7 Mar 31 2012 14:42:50
%S 0,0,0,0,14,23,17,47,31,79,49,119,71,167,97,223,127,41,46,359,199,439,
%T 241,527,82,89,337,727,391,839,449,137,73,1087,577,1223,647,1367,103,
%U 217,94,1679,881,1847,967,119,151,2207,1151,2399,1249,113,193,401,1457
%N a(n) = smallest k such that A000290(n+1) = A000290(n) + (A000290(n) mod k), or 0 if no such k exists.
%C a(n) is the "weight" of squares (A000290).
%C The decomposition of squares into weight * level + gap is A000217(n) = a(n) * A184221(n) + A005408(n) if a(n) > 0.
%H Remi Eismann, <a href="/A133150/b133150.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 1 we have A000290(n) = 1, A000290(n+1) = 4; there is no k such that 4 - 1 = 3 = (1 mod k), hence a(1) = 0.
%e For n = 5 we have A000290(n) = 25, A000290(n+1) = 36; 14 is the smallest k such that 36 - 25 = 11 = (25 mod k), hence a(5) = 14.
%e For n = 18 we have A000290(n) = 324, A000290(n+1) = 361; 41 is the smallest k such that 361 - 324 = 37 = (324 mod k), hence a(18) = 41.
%Y Cf. A020639, A117078, A117563, A001223, A118534, A090369, A090368, A130533, A130650, A130703, A130889, A130882.
%K nonn
%O 1,5
%A _Rémi Eismann_, Sep 22 2007 - Jan 10 2011
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