A304634 - OEIS

%I #11 May 17 2018 21:35:18

%S 4,6,9,10,12,14,15,18,20,21,22,24,25,26,28,33,34,35,36,38,39,40,44,45,

%T 46,48,49,50,51,52,54,55,56,57,58,60,62,63,65,68,69,72,74,75,76,77,80,

%U 82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,104

%N Numbers n with prime omicron 2, meaning A304465(n) = 2.

%C 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 This is a list of normalized factorizations (see A112798) of selected entries:

%e     4: {1,1}

%e     6: {1,2}

%e    12: {1,1,2}

%e    24: {1,1,1,2}

%e    36: {1,1,2,2}

%e    48: {1,1,1,1,2}

%e    60: {1,1,2,3}

%e    72: {1,1,1,2,2}

%e    96: {1,1,1,1,1,2}

%e   120: {1,1,1,2,3}

%e   144: {1,1,1,1,2,2}

%e   180: {1,1,2,2,3}

%e   192: {1,1,1,1,1,1,2}

%e   216: {1,1,1,2,2,2}

%e   240: {1,1,1,1,2,3}

%e   288: {1,1,1,1,1,2,2}

%e   384: {1,1,1,1,1,1,1,2}

%e   420: {1,1,2,3,4}

%e   432: {1,1,1,1,2,2,2}

%e   480: {1,1,1,1,1,2,3}

%e   576: {1,1,1,1,1,1,2,2}

%e   768: {1,1,1,1,1,1,1,1,2}

%e   840: {1,1,1,2,3,4}

%e   864: {1,1,1,1,1,2,2,2}

%e   960: {1,1,1,1,1,1,2,3}

%t Join@@Position[Table[Switch[n,1,0,_?PrimeQ,1,_,NestWhile[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],Length[#]>1&]//First],{n,100}],2]

%Y Cf. A001221, A001222, A001358, A005117, A007774, A007916, A055932, A071625, A112798, A181819, A182850, A182857, A275870, A304464, A304465, A304636, A304647.

%K nonn

%O 1,1

%A _Gus Wiseman_, May 15 2018