ラマヌジャンのタウ函数
τ ( n ) ≡ n − 610 σ 1231 ( n ) mod 3 6 for n ≡ 1 mod 3 {\displaystyle \tau (n)\equiv n^{-610}\sigma _{1231}(n)\ {\bmod {\ }}3^{6}{\text{ for }}n\equiv 1\ {\bmod {\ }}3}
τ ( n ) ≡ n − 610 σ 1231 ( n ) mod 3 7 for n ≡ 2 mod 3 {\displaystyle \tau (n)\equiv n^{-610}\sigma _{1231}(n)\ {\bmod {\ }}3^{7}{\text{ for }}n\equiv 2\ {\bmod {\ }}3}
τ ( n ) ≡ n − 30 σ 71 ( n ) mod 5 3 for n ≢ 0 mod 5 {\displaystyle \tau (n)\equiv n^{-30}\sigma _{71}(n)\ {\bmod {\ }}5^{3}{\text{ for }}n\not \equiv 0\ {\bmod {\ }}5}
τ ( n ) ≡ n σ 9 ( n ) mod 7 for n ≡ 0 , 1 , 2 , 4 mod 7 {\displaystyle \tau (n)\equiv n\sigma _{9}(n)\ {\bmod {\ }}7{\text{ for }}n\equiv 0,1,2,4\ {\bmod {\ }}7}