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A194763
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Number of k such that {k*2^(1/3)} > {n*2^(1/3)}, where { } = fractional part.
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3
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0, 0, 0, 3, 2, 1, 0, 6, 4, 2, 0, 9, 6, 3, 0, 12, 8, 4, 0, 15, 10, 5, 0, 18, 12, 6, 26, 19, 12, 5, 28, 20, 12, 4, 30, 21, 12, 3, 32, 22, 12, 2, 34, 23, 12, 1, 36, 24, 12, 0, 38, 25, 12, 52, 38, 24, 10, 53, 38, 23, 8, 54, 38, 22, 6, 55, 38, 21, 4, 56, 38, 20, 2, 57, 38, 19, 76
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OFFSET
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1,4
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LINKS
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MATHEMATICA
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r = 2^(1/3); p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194762 *)
Table[t[n], {n, 1, 100}] (* A194763 *)
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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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