

A194762


Number of k such that {k*2^(1/3)} < {n*2^(1/3)}, where { } = fractional part.


3



1, 2, 3, 1, 3, 5, 7, 2, 5, 8, 11, 3, 7, 11, 15, 4, 9, 14, 19, 5, 11, 17, 23, 6, 13, 20, 1, 9, 17, 25, 3, 12, 21, 30, 5, 15, 25, 35, 7, 18, 29, 40, 9, 21, 33, 45, 11, 24, 37, 50, 13, 27, 41, 2, 17, 32, 47, 5, 21, 37, 53, 8, 25, 42, 59, 11, 29, 47, 65, 14, 33, 52, 71, 17, 37
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..75.


MATHEMATICA

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 *)


CROSSREFS

Cf. A194763, A194738.
Sequence in context: A162609 A194752 A194740 * A054250 A193923 A198811
Adjacent sequences: A194759 A194760 A194761 * A194763 A194764 A194765


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 02 2011


STATUS

approved



