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a(n) = cardinality{ k<=n / A083054(k)=1}.
3

%I #9 May 09 2014 12:20:30

%S 1,1,1,1,1,2,2,3,3,3,4,4,5,5,6,6,6,7,7,8,8,8,8,8,9,9,10,10,10,10,10,

%T 11,11,12,12,12,13,13,14,14,14,14,14,15,15,16,16,16,16,16,17,17,18,18,

%U 18,18,18,19,19,20,20,20,21,21,22,22,22,22,22,23,23,24,24,24,24,24,25,25

%N a(n) = cardinality{ k<=n / A083054(k)=1}.

%H Boris Gourevitch, <a href="http://membres.lycos.fr/bgourevitch/temporaires/benoit/sqrt3fractal.jpg">Graph of A083057</a>

%F a(n) = n/3 + O(n) (it seems O(n) could be replaced with O(log(n))).

%o (PARI) {a(n)=if(n<1,0, sum(k=1,n,sqrtint(3*k^2)-3*sqrtint(k^2\3)==1))} /* _Michael Somos_, Aug 31 2006 */

%Y Cf. A083038, A083054, A083056, A083057.

%K nonn

%O 1,6

%A _Benoit Cloitre_, Apr 18 2003