: The Euler -function : Arithmetic Function 玡: Multiplicative Arithmetic Functions

# タ计计のタ计㎝

иノ multiplicative arithmetic function 阀├е―タ俱计ㄤタ计ぇ计のタ计㎝.

v(n) = 1.

Α種碞琌–Ω d 骸ì d| nd > 0 碞Ω, ┮礛眔 n タ计计.

Proposition 2.2.1   癸ヴ種 n ,  v(n) ボ n タ计计. 玥 v : 琌 multiplicative arithmetic function. τ璝 n = p1n1 ... prnr, ㄤい pi 钵借计, 玥 v(n) = (n1 + 1) ... (nr + 1).

v(n) = l(d ).

パ癸ヴ種 a, b , l(ab) = l(a)l(b) = 1, и l  (completely) multiplicative. パ Theorem 2.1.5v  multiplicative.

v(n) = v(p1n1) ... v(prnr) = (n1 + 1) ... (nr + 1).

(n) = d.

Α種碞琌–Ω d 骸ì d| nd > 0 碞 d, ┮礛眔 n タ计㎝.

Proposition 2.2.2   癸ヴ種 n ,  (n) ボ n タ计计. 玥 : 琌 multiplicative arithmetic function. τ璝 n = p1n1 ... prnr, ㄤい pi 钵借计, 玥

(n) = ... .

(n) = (d ).

パ癸ヴ種 a, b , (ab) = ab = (a)(b), и  (completely) multiplicative. パ Theorem 2.1.5  multiplicative.

(pt) = .

癸ヴ種 n , 璝 n = 1, и (n) = (1) = 1; τ璝 n = p1n1 ... prnr ㄤい pi 钵借计, 玥パ 琌 multiplicative 

(n) = (p1n1) ... (prnr) = ... .

(360) = = 15 . 13 . 6 = 1170.

: The Euler -function : Arithmetic Function 玡: Multiplicative Arithmetic Functions
Li 2007-06-28