This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325249 #5 Apr 17 2019 19:08:16
%S A325249 0,1,1,3,1,5,1,4,3,5,1,8,1,5,5,5,1,8,1,8,5,5,1,9,3,5,4,8,1,7,1,6,5,5,
%T A325249 5,7,1,5,5,9,1,7,1,8,8,5,1,10,3,8,5,8,1,9,5,9,5,5,1,12,1,5,8,7,5,7,1,
%U A325249 8,5,7,1,10,1,5,8,8,5,7,1,10,5,5,1,12,5
%N A325249 Sum of the omega-sequence of n.
%C A325249 We define the omega-sequence of n (row n of A323023) to have length A323014(n) = adjusted frequency depth of n, and the k-th term is Omega(red^{k-1}(n)), where Omega = A001222 and red^{k} is the k-th functional iteration of red = A181819, defined by red(n = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of n. For example, we have 180 -> 18 -> 6 -> 4 -> 3, so the omega-sequence of 180 is (5,3,2,2,1).
%F A325249 a(n) = A056239(A325248(n)).
%F A325249 a(n!) = A325274(n).
%e A325249 The omega-sequence of 180 is (5,3,2,2,1) with sum 13, so a(180) = 13.
%t A325249 omseq[n_Integer]:=If[n<=1,{},Total/@NestWhileList[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],Total[#]>1&]];
%t A325249 Table[Total[omseq[n]],{n,100}]
%Y A325249 Positions of m's are A000040 (m = 1), A001248 (m = 3), A030078 (m = 4), A068993 (m = 5), A050997 (m = 6), A325264 (m = 7).
%Y A325249 Cf. A056239, A118914, A181819, A182850, A323023, A325274.
%Y A325249 Omega-sequence statistics: A001222 (first omega), A001221 (second omega), A071625 (third omega), A323022 (fourth omega), A304465 (second-to-last omega), A182850 or A323014 (length/frequency depth), A325248 (Heinz number).
%K A325249 nonn
%O A325249 1,4
%A A325249 _Gus Wiseman_, Apr 16 2019