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noncube

Noncube is a term used to describe integers that are not perfect cubes. It is used in mathematics and related fields to categorize numbers not equal to k^3 for any integer k.

Formal definition: Let Z be the set of integers. A noncube is an integer that does not

Examples include 2, 3, 4, 5, 6, 7, 9, 10, -2, -3, -4, -5, -6, -7, etc.

There are infinitely many noncubes. Among natural numbers up to x, the number of noncubes is x

In number theory, the concept is often used when excluding perfect powers in problems or constructions, and

See also: perfect cube, cube, perfect power.

equal
k^3
for
any
integer
k.
The
set
of
cubes
is
{...,
-27,
-8,
-1,
0,
1,
8,
27,
64,
...}.
Cubes
include
-27,
-8,
-1,
0,
1,
8,
27,
64,
...;
for
instance,
8
is
a
cube
while
9
is
not.
−
floor(x^{1/3});
equivalently,
the
number
of
cubes
not
exceeding
x
is
floor(x^{1/3}).
Thus
the
density
of
noncubes
tends
to
1
as
x
grows,
since
cubes
have
growth
on
the
order
of
x^{1/3}.
it
generalizes
to
non-kth
powers
as
the
complement
of
k-th
powers.