NumberTheory
IsSquareFree
test whether an integer is square free
Calling Sequence
Parameters
Description
Examples
Compatibility
IsSquareFree(n)
n
-
nonzero integer
The IsSquareFree command returns true if n is square free and returns false if n is not square free.
An integer is said to be square free if it is not divisible by the square of another integer other than 1.
with⁡NumberTheory:
Any prime number is square free.
IsSquareFree⁡7
true
IsSquareFree⁡101
71407 is not square free since it is divisible by 1012.
IsSquareFree⁡71407
false
irem⁡71407,1012
0
The Tabulate command can be used to display square-free numbers in a grid. The following table highlights all square-free numbers from 1 to 100 with a pink background.
V ≔ r,c→DocumentTools:-Tabulate⁡Matrix⁡r,c,i,j→c*i − 1+j,fillcolor=T,i,j→`if`⁡IsSquareFree⁡c*i − 1+j,Pink,White:
V⁡10,10
Tabulate
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Note that V(r, c) can be modified to show tables for various values of r and c.
The NumberTheory[IsSquareFree] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
ifactor
isprime
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