a(n) is the least k > 0 such that sigma(k!) >= n*k!.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =9a(5) =14a(6) =23a(7) =43a(8) =79a(9) =149a(10) =263a(11) =461a(12) =823a(13) =1451a(14) =2549a(15) =4483a(16) =7879a(17) =13859a(18) =24247a(19) =42683a(20) =75037a(21) =131707a(22) =230773a(23) =405401a(24) =710569a(25) =1246379a(26) =2185021a(27) =3831913a(28) =6720059a(29) =11781551