a(n) = sopfr(n!), where sopfr = A001414 is the integer log.

Terms

a(0) =0a(1) =0a(2) =2a(3) =5a(4) =9a(5) =14a(6) =19a(7) =26a(8) =32a(9) =38a(10) =45a(11) =56a(12) =63a(13) =76a(14) =85a(15) =93a(16) =101a(17) =118a(18) =126a(19) =145a(20) =154a(21) =164a(22) =177a(23) =200a(24) =209a(25) =219a(26) =234a(27) =243a(28) =254a(29) =283