Ivan Neretin, David A. Corneth, and Charles R Greathouse IV, Table of n, a(n) for n = 1..344 (1..208 from Neretin, 209..266 from Corneth, 267..344 from Greathouse)
Let k = number of prime divisors of n! counted with multiplicity; b = number of distinct prime divisors of n!. Then n is in sequence if k/b is an integer.
EXAMPLE
S(4!) = bigomega(4!) / omega(4!) = 4/2 = 2 so 4 is 3rd term in the sequence.
MATHEMATICA
ointQ[n_]:=Module[{f=n!}, IntegerQ[PrimeOmega[f]/PrimeNu[f]]]; Select[Range[ 2, 6000], ointQ] (* Harvey P. Dale, Dec 07 2013 *)
Omega = Nu = 0; a = {}; Do[If[PrimeQ[n], Nu++]; Omega += PrimeOmega[n];
If[Divisible[Omega, Nu], AppendTo[a, n]], {n, 2, 6000}]; a (* Ivan Neretin, Mar 14 2017 *)
