Square-free integers: Difference between revisions

=={{header|FreeBASIC}}==

<lang freebasic>' version 06-07-2018

' compile with: fbc -s console

Const As ULongInt trillion = 1000000000000ull

Const As ULong max = Sqr(trillion + 145)

Dim As UByte list(), sieve()

Dim As ULong prime()

ReDim list(max), prime(max\12), sieve(max)

Dim As ULong a, b, c, i, k, stop_ = Sqr(max)

For i = 4 To max Step 2 ' prime sieve remove even numbers except 2

sieve(i) = 1

Next

For i = 3 To stop_ Step 2 ' proces odd numbers

If sieve(i) = 0 Then

For a = i * i To max Step i * 2

sieve(a) = 1

Next

End If

Next

For i = 2 To max ' move primes to a list

If sieve(i) = 0 Then

c += 1

prime(c) = i

End If

Next

ReDim sieve(145): ReDim Preserve prime(c)

For i = 1 To c ' find all square free integers between 1 and 1000000

a = prime(i) * prime(i)

If a > 1000000 Then Exit For

For k = a To 1000000 Step a

list(k) = 1

Next

Next

k = 0

For i = 1 To 145 ' show all between 1 and 145

If list(i) = 0 Then

Print Using"####"; i;

k +=1

If k Mod 20 = 0 Then Print

End If

Next

Print : Print

sieve(0) = 1 ' = trillion

For i = 1 To 5 ' process primes 2, 3, 5, 7, 11

a = prime(i) * prime(i)

b = a - trillion Mod a

For k = b To 145 Step a

sieve(k) = 1

Next

Next

For i = 6 To c ' process the rest of the primes

a = prime(i) * prime(i)

k = a - trillion Mod a

If k <= 145 Then sieve(k) = 1

Next

k = 0

For i = 0 To 145

If sieve(i) = 0 Then

Print Using "################"; (trillion + i);

k += 1

If k Mod 5 = 0 Then print

End If

Next

Print : Print

a = 1 : b = 100 : k = 0

Do Until b > 1000000 ' count them

For i = a To b

If list(i) = 0 Then k += 1

Next

Print "There are "; k; " square free integers between 1 and "; b

a = b : b *= 10

Loop

' empty keyboard buffer

While Inkey <> "" : Wend

Print : Print "hit any key to end program"

Sleep

End</lang>

{{out}}

<pre> 1 2 3 5 6 7 10 11 13 14 15 17 19 21 22 23 26 29 30 31

33 34 35 37 38 39 41 42 43 46 47 51 53 55 57 58 59 61 62 65

66 67 69 70 71 73 74 77 78 79 82 83 85 86 87 89 91 93 94 95

97 101 102 103 105 106 107 109 110 111 113 114 115 118 119 122 123 127 129 130

131 133 134 137 138 139 141 142 143 145

1000000000001 1000000000002 1000000000003 1000000000005 1000000000006

1000000000007 1000000000009 1000000000011 1000000000013 1000000000014

1000000000015 1000000000018 1000000000019 1000000000021 1000000000022

1000000000023 1000000000027 1000000000029 1000000000030 1000000000031

1000000000033 1000000000037 1000000000038 1000000000039 1000000000041

1000000000042 1000000000043 1000000000045 1000000000046 1000000000047

1000000000049 1000000000051 1000000000054 1000000000055 1000000000057

1000000000058 1000000000059 1000000000061 1000000000063 1000000000065

1000000000066 1000000000067 1000000000069 1000000000070 1000000000073

1000000000074 1000000000077 1000000000078 1000000000079 1000000000081

1000000000082 1000000000085 1000000000086 1000000000087 1000000000090

1000000000091 1000000000093 1000000000094 1000000000095 1000000000097

1000000000099 1000000000101 1000000000102 1000000000103 1000000000105

1000000000106 1000000000109 1000000000111 1000000000113 1000000000114

1000000000115 1000000000117 1000000000118 1000000000119 1000000000121

1000000000122 1000000000123 1000000000126 1000000000127 1000000000129

1000000000130 1000000000133 1000000000135 1000000000137 1000000000138

1000000000139 1000000000141 1000000000142 1000000000145

There are 61 square free integers between 1 and 100

There are 608 square free integers between 1 and 1000

There are 6083 square free integers between 1 and 10000

There are 60794 square free integers between 1 and 100000

There are 607926 square free integers between 1 and 1000000</pre>