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NumberTheory

  

IsSquareFree

  

test whether an integer is square free

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsSquareFree(n)

Parameters

n

-

nonzero integer

Description

• 

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.

Examples

withNumberTheory:

Any prime number is square free.

IsSquareFree7

true

(1)

IsSquareFree101

true

(2)

71407 is not square free since it is divisible by 1012.

IsSquareFree71407

false

(3)

irem71407,1012

0

(4)

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.

Vr,c→DocumentTools:-TabulateMatrixr,c,i,j→c*i1+j,fillcolor=T,i,j→`if`IsSquareFreec*i1+j,Pink,White:

V10,10

Tabulate

(5)

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

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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.

Compatibility

• 

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

NumberTheory