Added prime-omega
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@ -23,6 +23,7 @@
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divisors
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prime-divisors
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prime-exponents
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prime-omega
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; roots
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integer-root
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@ -489,6 +490,12 @@
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(map (inst cadr N N (Listof N))
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(prime-divisors/exponents n)))
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(: prime-omega : N -> N)
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; http://reference.wolfram.com/mathematica/ref/PrimeOmega.html
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(define (prime-omega n)
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(for/fold: ([sum : Natural 0]) ([e (in-list (prime-exponents n))])
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(+ sum e)))
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(: integer-root/remainder : N N -> (Values N N))
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(define (integer-root/remainder a n)
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@ -539,6 +539,15 @@ all divisors of @racket[n].
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(apply + (map sqr (divisors 12)))]
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}
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@margin-note{OEIS: @hyperlink["http://oeis.org/A001222"]{Big Omega}}
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@defproc[(prime-omega [n Natural]) natural?]{
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Counting multiplicities the number of prime factors of @racket[n] is returned.
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Note: The function @racket[prime-omega] is multiplicative.
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@interaction[#:eval untyped-eval
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(prime-omega (* 2 2 2 3 3 4 5))]
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}
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@; ----------------------------------------
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@section[#:tag "number-sequences"]{Number Sequences}
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