252

252 is: the central binomial coefficient ( 10 5 ) {\displaystyle {\tbinom {10}{5}}}, the largest one divisible by all coefficients in the previous line τ ( 3 ) {\displaystyle \tau (3)}, where τ {\displaystyle \tau } is the Ramanujan tau function. σ 3 ( 6 ) {\displaystyle \sigma _{3}(6)}, where σ 3 {\displaystyle \sigma _{3}} is the function that sums the cubes of the divisors of its argument: 1 3 + 2 3 + 3 3 + 6 3 = ( 1 3 + 2 3 ) ( 1 3 + 3 3 ) = 252. {\displaystyle 1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.}