%I #6 Jul 18 2023 23:25:37

%S 2,4,6,8,12,16,18,24,32,36,40,48,54,64,72,80,96,108,120,128,144,160,

%T 162,192,216,224,240,256,288,320,324,360,384,432,448,480,486,512,576,

%U 640,648,672,720,768,800,864,896,960,972,1024,1080,1152,1280,1296,1344

%N Numbers whose rounded-down (floor) mean of prime factors (with multiplicity) is 2.

%e The terms together with their prime factors begin:

%e 2 = 2

%e 4 = 2*2

%e 6 = 2*3

%e 8 = 2*2*2

%e 12 = 2*2*3

%e 16 = 2*2*2*2

%e 18 = 2*3*3

%e 24 = 2*2*2*3

%e 32 = 2*2*2*2*2

%e 36 = 2*2*3*3

%e 40 = 2*2*2*5

%e 48 = 2*2*2*2*3

%e 54 = 2*3*3*3

%e 64 = 2*2*2*2*2*2

%e 72 = 2*2*2*3*3

%e 80 = 2*2*2*2*5

%e 96 = 2*2*2*2*2*3

%t prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];

%t Select[Range[100],Floor[Mean[prifacs[#]]]==2&]

%Y Without multiplicity we appear to have A007694.

%Y Prime factors are listed by A027746, indices A112798.

%Y Positions of 2's in A126594, positions of first appearances A364037.

%Y For prime indices and ceiling we have A363950, counted by A026905.

%Y For prime indices we have A363954 (or A363949), counted by A363745.

%Y A078175 lists numbers with integer mean of prime factors.

%Y A123528/A123529 gives mean of prime factors, indices A326567/A326568.

%Y A316413 ranks partitions with integer mean, counted by A067538.

%Y A363895 gives floor of mean of distinct prime factors.

%Y A363943 gives floor of mean of prime indices, ceiling A363944.

%Y Cf. A001222, A056239, A327473, A327476, A360013, A360015, A363488, A363945.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jul 18 2023