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A304636 Numbers n with prime omicron 3, meaning A304465(n) = 3.

%I A304636 #6 May 17 2018 21:35:26
%S A304636 8,27,30,42,66,70,78,102,105,110,114,125,130,138,154,165,170,174,182,
%T A304636 186,190,195,222,230,231,238,246,255,258,266,273,282,285,286,290,310,
%U A304636 318,322,343,345,354,357,360,366,370,374,385,399,402,406,410,418,426
%N A304636 Numbers n with prime omicron 3, meaning A304465(n) = 3.
%C A304636 If n > 1 is not a prime number, we have A056239(n) >= Omega(n) >= omega(n) >= A071625(n) >= ... >= omicron(n) > 1 where Omega = A001222, omega = A001221, and omicron = A304465.
%e A304636 This is a list of normalized factorizations (see A112798) of selected entries:
%e A304636      8: {1,1,1}
%e A304636     30: {1,2,3}
%e A304636    360: {1,1,1,2,2,3}
%e A304636    720: {1,1,1,1,2,2,3}
%e A304636    900: {1,1,2,2,3,3}
%e A304636   1440: {1,1,1,1,1,2,2,3}
%e A304636   2160: {1,1,1,1,2,2,2,3}
%e A304636   2880: {1,1,1,1,1,1,2,2,3}
%e A304636   4320: {1,1,1,1,1,2,2,2,3}
%e A304636   5760: {1,1,1,1,1,1,1,2,2,3}
%e A304636   8640: {1,1,1,1,1,1,2,2,2,3}
%e A304636 Starting with A112798(1801800) and repeatedly taking the multiset of multiplicities we have {1,1,1,2,2,3,3,4,5,6} -> {1,1,1,2,2,3} -> {1,2,3} -> {1,1,1} -> {3}, so 1801800 belongs to the sequence.
%t A304636 Join@@Position[Table[Switch[n,1,0,_?PrimeQ,1,_,NestWhile[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],Length[#]>1&]//First],{n,200}],3]
%Y A304636 Cf. A001221, A001222, A005117, A007916, A014612, A033992, A071625, A112798, A181819, A182850, A182857, A304464, A304465, A304634, A304647.
%K A304636 nonn
%O A304636 1,1
%A A304636 _Gus Wiseman_, May 15 2018