Radical of an integer: Difference between revisions

=={{header|FreeBASIC}}==

{{trans|XPL0}}

<syntaxhighlight lang="vb">'#include "isprime.bas"

Function Radical(n As Integer) As Integer 'Return radical of n

Dim As Integer d = 2, d0 = 0, p = 1

While n >= d*d

While n Mod d = 0

If d <> d0 Then

p *= d

d0 = d

End If

n /= d

Wend

d += 1

Wend

If d <> d0 Then p *= n

Return p

End Function

Function DistinctFactors(n As Integer) As Integer 'Return count of distinct factors of n

Dim As Integer d = 2, d0 = 0, c = 0

While n >= d*d

While n Mod d = 0

If d <> d0 Then

c += 1

d0 = d

End If

n = n/d

Wend

d += 1

Wend

If d <> d0 And n <> 1 Then c += 1

Return c

End Function

Dim As Integer n, c, count(0 To 9), pcount, ppcount, p2, p

Print "The radicals for the first 50 positive integers are:"

For n = 1 To 50

Print Using "####"; Radical(n);

If n Mod 10 = 0 Then Print

Next

Print Using !"\nRadical for ###,###: ###,###"; 99999; Radical(99999)

Print Using "Radical for ###,###: ###,###"; 499999; Radical(499999)

Print Using "Radical for ###,###: ###,###"; 999999; Radical(999999)

For n = 0 To 9

count(n) = 0

Next

For n = 1 To 1e6

c = DistinctFactors(n)

count(c) += 1

Next

Print !"\nBreakdown of numbers of distinct prime factors \nfor positive integers from 1 to 1,000,000:"

c = 0

For n = 0 To 9

If count(n) > 0 Then Print Using " #: ###,###"; n; count(n)

c += count(n)

Next

Print Using !" ---------\n #,###,###"; c

Print !"\nor graphically:\n"; String(50, "-")

For n = 0 To 9

If count(n) > 0 Then Print n; " "; String(count(n)/1e4, Chr(177)); " "; count(n)

c += count(n)

Next

Print String(50, "-")

'Bonus (algorithm from Wren):

pcount = 0

For n = 1 To 1e6

If isPrime(n) Then pcount += 1

Next

Print !"\nFor primes or powers (>1) thereof <= 1,000,000:"

Print Using " Number of primes: ##,###"; pcount

ppcount = 0

For p = 1 To Sqr(1e6)

If isPrime(p) Then

p2 = p

Do

p2 *= p

If p2 > 1e6 Then Exit Do

ppcount += 1

Loop

End If

Next

Print Using " Number of powers: ##,###"; ppcount

Print Using "Add 1 for number 1: ##,###"; 1

If isPrime(n) Then pcount += 1

Print Spc(19); "-------"

Print Spc(13); Using !"Total: ##,###"; pcount + ppcount + 1

Sleep</syntaxhighlight>

{{out}}

<pre>The radicals for the first 50 positive integers are:

1 2 3 2 5 6 7 2 3 10

11 6 13 14 15 2 17 6 19 10

21 22 23 6 5 26 3 14 29 30

31 2 33 34 35 6 37 38 39 10

41 42 43 22 15 46 47 6 7 10

Radical for 99,999: 33,333

Radical for 499,999: 3,937

Radical for 999,999: 111,111

Breakdown of numbers of distinct prime factors

for positive integers from 1 to 1,000,000:

0: 1

1: 78,734

2: 288,726

3: 379,720

4: 208,034

5: 42,492

6: 2,285

7: 8

---------

1,000,000

or graphically:

--------------------------------------------------

0 1

1 ▒▒▒▒▒▒▒▒ 78734

2 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 288726

3 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 379720

4 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ 208034

5 ▒▒▒▒ 42492

6 2285

7 8

--------------------------------------------------

For primes or powers (>1) thereof <= 1,000,000:

Number of primes: 78,498

Number of powers: 236

Add 1 for number 1: 1

-------

Total: 78,735</pre>