Reference links
\ (number theoretic symbols and function template: \)
\ (symbol: \)
\ (s plus: \) \ (\ sum_ {I =. 1} ^ {n-} I \)
\ (multiplicative: \) \ ( \ prod_. 1 = {I}} ^ {n-I \)
\ (divisible: (p is a factor q) P | q \)
\ (function \)
\ (Euler function: \) \ (\ varphi (n-) n-* = \ prod_. 1 = {I} ^ {K} \ left (l- \ FRAC. 1 {{}}} I {P_ \ right) \)
\ (Conclusion: a ^ {\ varphi (p )} \ equiv 1 \ quad (\ bmod p) \)
\ (Möbius function (function Mobius): \ MU (D) = (-. 1) ^ {K} \)
\ (\ MU (n-) = \ left \ {\ Array the begin {{} {L}. 1 }, \ space if n is equal to 1 \\ {(-1) ^ { k}}, if n is the number of non-factor and the square of n = p1 * p2 ⋅⋅⋅pk \\ { 0}, if there are n squared factor \ end {array} \ right. \)
\ (Dirichlet product (Dirichlet convolution), (f * g) (n) = \ sum_ {d | n} f (d) * g \ left (\ frac {n} {d} \ right) \)
\ (Mobius inversion: f (n) = \ sum_ {d | n} g (d) \)
\ (Du teach sieve: On a known number of function f (n), now requires S (n) = \ sum_ {i = 1} ^ {n} f (i) \)