Documentation

>>> primeFactors 60
[2,2,3,5]
>>> primeFactors 0
[]
>>> primeFactors 1
[]
>>> primeFactors 2
[2]
>>> primeFactors 2147483647
[2147483647]
>>> primeFactors 999999999989
[999999999989]
>>> primeFactors 999999999997
[5507,181587071]

>>> isPrime 4649
True
>>> isPrime 0
False
>>> isPrime 1
False
>>> isPrime 2
True
>>> isPrime 2147483647
True
>>> isPrime 999999999989
True
>>> isPrime 999999999997
False

\n -> not (n >= 0) || totient n == length [x|x<-[1..n], gcd n x == 1]

+++ OK, passed 100 tests.

>>> totient 0
0
>>> totient 1
1

>>> divisors 12
[1,2,3,4,6,12]
>>> divisors 0
[1]
>>> divisors 1
[1]
>>> length (divisors 735134400)
1344

>>> moebius 1
1
>>> moebius 2
-1
>>> moebius 3
-1
>>> moebius (2 * 2)
0
>>> moebius (2 * 3)
1
>>> moebius (2 * 2 * 3)
0

>>> moebiusInversion 12 (length.divisors)
fromList [(1,1),(2,1),(3,1),(4,1),(6,1),(12,1)]
>>> moebiusInversion 999999999997 (length.divisors)
fromList [(1,1),(5507,1),(181587071,1),(999999999997,1)]
>>> IM.size $ moebiusInversion 735134400 (length.divisors)
1344