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A309262 a(0) = 0, a(1) = 1, and for any n > 1, a(n) = Sum_{k > 1} a(floor(n/k^2)).

%I A309262 #13 Jul 22 2019 12:00:23
%S A309262 0,1,0,0,1,1,1,1,0,1,1,1,1,1,1,1,3,3,2,2,2,2,2,2,2,3,3,3,3,3,3,3,1,1,
%T A309262 1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,
%U A309262 8,8,8,8,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7
%N A309262 a(0) = 0, a(1) = 1, and for any n > 1, a(n) = Sum_{k > 1} a(floor(n/k^2)).
%C A309262 For any n > 1 and k > A000196(n), a(floor(n/k^2)) = a(0) = 0, hence the series in the name is well defined.
%C A309262 This sequence is a variant of A022825; here we sum terms of the form a(floor(n/k^2)), there terms of the form a(floor(n/k)).
%H A309262 Rémy Sigrist, <a href="/A309262/b309262.txt">Table of n, a(n) for n = 0..10000</a>
%e A309262 a(5) = a(floor(5/2^2)) = a(1) = 1.
%t A309262 Join[{0}, Clear[a]; a[0]=0; a[1]=1; a[n_]:=a[n]=Sum[a[Floor[n/k^2]], {k, 2, n}]; Table[a[n], {n, 1, 100}]] (* _Vincenzo Librandi_, Jul 22 2019 *)
%o A309262 (PARI) a(n) = if (n<=1, n, sum (k=2, sqrtint(n), a(n\k^2)))
%Y A309262 Cf. A000196, A022825.
%K A309262 nonn
%O A309262 0,17
%A A309262 _Rémy Sigrist_, Jul 19 2019