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Ingy döt Net 2025-08-11 18:05:26 -07:00
parent 4d5544505c
commit 4924dd0264
3073 changed files with 55820 additions and 4408 deletions
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46
Task/Totient-function/Agena/totient-function.agena Normal file
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scope # Totient function
# returns the number of integers k where 1 <= k <= n that are mutually prime to n
local procedure totient( n :: number ) :: number
if n < 3 then result := 1
elif n = 3 then result := 2
else
result := n;
local v, i := n, 2;
while i * i <= v do
if v mod i = 0 then
while v mod i = 0 do v \:= i od;
result -:= result \ i
fi;
if i = 2 then
i := 1
fi;
i +:= 2
od;
if v > 1 then result -:= result \ v fi;
fi;
return result
end;
# show the totient function values for the first 25 integers
io.write( " n phi(n) remarks\n" );
for n to 25 do
local constant tn := totient( n );
printf( "%2d: %5d%s\n", n, tn, if tn = n - 1 and tn <> 0 then " n is prime" else "" fi )
od;
# use the totient function to count primes
local n100, n1_000, n10_000, n100_000 := 0, 0, 0, 0;
for n to 100_000 do
if totient( n ) = n - 1 then
if n <= 100 then n100 +:= 1 fi;
if n <= 1000 then n1_000 +:= 1 fi;
if n <= 10000 then n10_000 +:= 1 fi;
if n <= 100000 then n100_000 +:= 1 fi
fi
od;
printf( "There are %6d primes below 100\n", n100 );
printf( "There are %6d primes below 1 000\n", n1_000 );
printf( "There are %6d primes below 10 000\n", n10_000 );
printf( "There are %6d primes below 100 000\n", n100_000 )
end