diff --git a/pkgs/math-pkgs/math-doc/math/scribblings/math-number-theory.scrbl b/pkgs/math-pkgs/math-doc/math/scribblings/math-number-theory.scrbl index ec7c24ef7b..2d48f06f12 100644 --- a/pkgs/math-pkgs/math-doc/math/scribblings/math-number-theory.scrbl +++ b/pkgs/math-pkgs/math-doc/math/scribblings/math-number-theory.scrbl @@ -517,9 +517,9 @@ square, otherwise @racket[#f]. } @; ---------------------------------------- -@section[#:tag "multiplicative"]{Multiplicative Functions} +@section[#:tag "multiplicative"]{Multiplicative and Arithmetic Functions} -The functions in this section are @deftech{multiplicative}. +The functions in this section are @deftech{multiplicative} (with exception of the Von Mangoldt function). In number theory, a multiplicative function is a function @racket[f] such that @racket[(f (* a b)) = (* (f a) (f b))] for all coprime natural numbers @racket[a] and @racket[b]. @@ -573,6 +573,8 @@ The von Mangoldt function. If @racket[n=p^k] for a prime @racket[p] and an integer @racket[k>=1] then @racket[(log n)] is returned. Otherwise 0 is returned. +Note: The Von Mangoldt function is not multiplicative. + @interaction[#:eval untyped-eval (mangoldt-lambda (* 3 3)) (log 3)]