Radical of an integer: Difference between revisions
Added Lua
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(Added Lua) |
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Overall total: 78735
</pre>
=={{header|Lua}}==
{{Trans|ALGOL 68}}
<syntaxhighlight lang="lua">
do -- find the radicals of some integers - the radical of n is the product
-- of the distinct prime factors of n, the radical of 1 is 1
local maxNumber = 1000000; -- maximum number we will consider
local upfc, radical = {}, {} -- unique prime factor counts and radicals
for i = 1, maxNumber do
upfc[ i ] = 0
radical[ i ] = 1
end
for i = 2, maxNumber do
if upfc[ i ] == 0 then
radical[ i ] = i
upfc[ i ] = 1
for j = i + i, maxNumber, i do
upfc[ j ] = upfc[ j ] + 1
radical[ j ] = radical[ j ] * i
end
end
end
-- show the radicals of the first 50 positive integers
io.write( "Radicals of 1 to 50:\n" )
for i = 1, 50 do
io.write( string.format( "%5d", radical[ i ] ), ( i % 10 == 0 and "\n" or "" ) )
end
-- radicals of some specific numbers
io.write( "\n" )
io.write( "Radical of 99999: ", radical[ 99999 ], "\n" )
io.write( "Radical of 499999: ", radical[ 499999 ], "\n" )
io.write( "Radical of 999999: ", radical[ 999999 ], "\n" )
io.write( "\n" )
-- show the distribution of the unique prime factor counts
local dpfc = {}
for i = 1, maxNumber do
local count = dpfc[ upfc[ i ] ]
dpfc[ upfc[ i ] ] = ( count == null and 1 or count + 1 )
end
io.write( "Distribution of radicals:\n" )
for i = 0, #dpfc do
io.write( string.format( "%2d", i ), ": ", dpfc[ i ], "\n" )
end
end
</syntaxhighlight>
{{out}}
<pre>
Radicals of 1 to 50:
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 of 99999: 33333
Radical of 499999: 3937
Radical of 999999: 111111
Distribution of radicals:
0: 1
1: 78734
2: 288726
3: 379720
4: 208034
5: 42492
6: 2285
7: 8
</pre>
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