π ( n ) = ∑ m = 1 n ( 1 − ⌊ ⌊ ( m ! ) 2 m 3 ⌋ ( m ! ) 2 m 3 ⌋ ) = n − ∑ m = 1 n ⌊ ⌊ ( m ! ) 2 m 3 ⌋ ( m ! ) 2 m 3 ⌋ = ∑ m = 1 n − ⌊ ⌊ ( m ! ) 2 m 3 ⌋ − ( m ! ) 2 m 3 ⌋ = | ∑ m = 1 n ⌊ ⌊ ( m ! ) 2 m 3 ⌋ − ( m ! ) 2 m 3 ⌋ | = ∑ m = 1 n | ⌊ ⌊ ( m ! ) 2 m 3 ⌋ − ( m ! ) 2 m 3 ⌋ | {\displaystyle \pi \left(n\right)=\sum _{m=1}^{n}{\left(1-\left\lfloor {\frac {\left\lfloor {\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor }{\frac {\left(m!\right)^{2}}{m^{3}}}}\right\rfloor \right)}=n-\sum _{m=1}^{n}{\left\lfloor {\frac {\left\lfloor {\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor }{\frac {\left(m!\right)^{2}}{m^{3}}}}\right\rfloor }=\sum _{m=1}^{n}-\left\lfloor \left\lfloor {\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor -{\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor =\left|\sum _{m=1}^{n}\left\lfloor \left\lfloor {\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor -{\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor \right|=\sum _{m=1}^{n}\left|\left\lfloor \left\lfloor {\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor -{\frac {\left(m!\right)^{2}}{m^{3}}}\right\rfloor \right|}
