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A325238 First positive integer with each omega-sequence.

%I A325238 #6 Apr 16 2019 15:26:05
%S A325238 1,2,4,6,8,12,16,24,30,32,36,48,60,64,96,120,128,192,210,216,240,256,
%T A325238 360,384,420,480,512,720,768,840,900,960,1024,1260,1296,1440,1536,
%U A325238 1680,1920,2048,2310,2520,2880,3072,3360,3840,4096,4620,5040,5760,6144,6720
%N A325238 First positive integer with each omega-sequence.
%C A325238 We define the omega-sequence of n (row n of A323023) to have length A323014(n) = frequency depth of n, and the k-th part is Omega(red^{k-1}(n)), where Omega = A001222 and red^{k} is the k-th functional iteration of red = A181819, given by red(n = p^i*...*q^j) = prime(i)*...*prime(j), i.e., the product of primes indexed by the prime exponents of n.
%e A325238 The sequence of terms together with their omega-sequences begins:
%e A325238     1:
%e A325238     2: 1
%e A325238     4: 2 1
%e A325238     6: 2 2 1
%e A325238     8: 3 1
%e A325238    12: 3 2 2 1
%e A325238    16: 4 1
%e A325238    24: 4 2 2 1
%e A325238    30: 3 3 1
%e A325238    32: 5 1
%e A325238    36: 4 2 1
%e A325238    48: 5 2 2 1
%e A325238    60: 4 3 2 2 1
%e A325238    64: 6 1
%e A325238    96: 6 2 2 1
%e A325238   120: 5 3 2 2 1
%e A325238   128: 7 1
%e A325238   192: 7 2 2 1
%e A325238   210: 4 4 1
%e A325238   216: 6 2 1
%e A325238   240: 6 3 2 2 1
%e A325238   256: 8 1
%e A325238   360: 6 3 3 1
%e A325238   384: 8 2 2 1
%e A325238   420: 5 4 2 2 1
%t A325238 tomseq[n_]:=If[n<=1,{},Most[FixedPointList[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]]]]];
%t A325238 omseqs=Table[Total/@tomseq[n],{n,1000}];
%t A325238 Sort[Table[Position[omseqs,x][[1,1]],{x,Union[omseqs]}]]
%Y A325238 Cf. A001221, A001222, A007916, A011784, A070175, A071625, A118914, A181819, A181821, A303555, A304465, A323014, A323023, A325238, A325239.
%K A325238 nonn
%O A325238 1,2
%A A325238 _Gus Wiseman_, Apr 14 2019