• Day algorithm [more] • The fifth thirteen literacy: What is a multiplicative function?

▎ unique decomposition theorem

　　You may ask, learn multiplicative function, why mention the unique decomposition theorem it? God-Malaysia relations? After the text is useful, please patience to watch.

　　The only major decomposition theorem means that a certain number x can be divided into a number of product quality (except what 1,0), this is replaced by the equation:

　　n=a₁^p1·a₂^p2·a₃^p3·a₄^p4·a₅^p5·……

　　This is actually very simple, which is the prime factor decomposition of principle.

▎ number theory function

　　Of little value, direct throw define, in fact, usually do with them as a function of eighth grade the same, but without tables, images represent it.

　　In number theory , the arithmetic functions (also known as number theory function) refers to the domain is a positive integer , accompany domain is a complex of functions , each function can be regarded as a complex number arithmetic sequence .

　　The most important function is the product of the arithmetic and additive function. The most important function is the arithmetic operation of Dirichlet convolution, set for arithmetic functions, with its multiplication, the general function of the addition of addition can be obtained a Abel ring . (Copy from Baidu Encyclopedia)

▎ multiplicative function

　　For a function F, if it satisfies f (ab) = f (a) (b), we call multiplicative function.

　　Then the only decomposition theorem comes in handy:

　　若n=a ₁ ^p1·a ₂ ^p2·a ₃ ^p3·a ₄ ^p4·a ₅ ^p5·……

　　Then there are F (n-) = F (A _{. 1} ^P1 ) · F (A ₂ ^P2 ) · F (A _{. 3} ^P3 ) · F (A _{. 4} ^P4 ) · F (A _{. 5} ^P5 ) · ......

　　Such a evaluation function have another way of.