numbers (version 0.5-6)

omega: Number of Prime Factors

Description

Sum of all exponents of prime factors in the prime decomposition.

Usage

omega(n)
Omega(n)

Arguments

n

Positive integer.

Value

• Natural number.

Details

Compute the number of prime factors of n resp. the sum of their exponents in the prime decomposition.

(-1)^Omega(n) is the Liouville function.

See Also

sigma

Examples

omega(2*3*5*7*11*13*17*19)  #=> 8
Omega(2 * 3^2 * 5^3 * 7^4)  #=> 10

stopifnot(identical(sapply(1:16, omega),
                    c(0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1)))
stopifnot(identical(sapply(1:16, Omega),
                    c(0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4)))