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A309262
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a(0) = 0, a(1) = 1, and for any n > 1, a(n) = Sum_{k > 1} a(floor(n/k^2)).
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2
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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, 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, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7
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OFFSET
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0,17
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COMMENTS
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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.
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)).
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LINKS
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EXAMPLE
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a(5) = a(floor(5/2^2)) = a(1) = 1.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = if (n<=1, n, sum (k=2, sqrtint(n), a(n\k^2)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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