Number of Prime Factors
Number of prime factors resp. sum of all exponents of prime factors in the prime decomposition.
omega(n) Omega(n)
n |
Positive integer. |
'omega(n)' returns the number of prime factors of 'n' while 'Omega(n)' returns the sum of their exponents in the prime decomposition. 'omega' and 'Omega' are identical if there are no quadratic factors.
Remark: (-1)^Omega(n) is the Liouville function.
Natural number.
Works well up to 10^9.
omega(2*3*5*7*11*13*17*19) #=> 8 Omega(2 * 3^2 * 5^3 * 7^4) #=> 10
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