a(n) is the lowest nonnegative exponent k such that n!^k is the product of the divisors of n!.

Terms

a(0) =0a(1) =1a(2) =2a(3) =4a(4) =8a(5) =15a(6) =30a(7) =48a(8) =80a(9) =135a(10) =270a(11) =396a(12) =792a(13) =1296a(14) =2016a(15) =2688a(16) =5376a(17) =7344a(18) =14688a(19) =20520a(20) =30400a(21) =48000a(22) =96000a(23) =121440a(24) =170016a(25) =266112a(26) =338688a(27) =458640a(28) =917280a(29) =1166400