A364157 Numbers whose rounded-down (floor) mean of prime factors (with multiplicity) is 2.

2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 40, 48, 54, 64, 72, 80, 96, 108, 120, 128, 144, 160, 162, 192, 216, 224, 240, 256, 288, 320, 324, 360, 384, 432, 448, 480, 486, 512, 576, 640, 648, 672, 720, 768, 800, 864, 896, 960, 972, 1024, 1080, 1152, 1280, 1296, 1344

Offset: 1

Author

Gus Wiseman, Jul 18 2023

Keywords

• nonn

Examples

			The terms together with their prime factors begin:
   2 = 2
   4 = 2*2
   6 = 2*3
   8 = 2*2*2
  12 = 2*2*3
  16 = 2*2*2*2
  18 = 2*3*3
  24 = 2*2*2*3
  32 = 2*2*2*2*2
  36 = 2*2*3*3
  40 = 2*2*2*5
  48 = 2*2*2*2*3
  54 = 2*3*3*3
  64 = 2*2*2*2*2*2
  72 = 2*2*2*3*3
  80 = 2*2*2*2*5
  96 = 2*2*2*2*2*3
		

Crossrefs

Without multiplicity we appear to have A007694.

Prime factors are listed by A027746, indices A112798.

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

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

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

A078175 lists numbers with integer mean of prime factors.

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

A316413 ranks partitions with integer mean, counted by A067538.

A363895 gives floor of mean of distinct prime factors.

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

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

Programs

Mathematica

prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
Select[Range[100],Floor[Mean[prifacs[#]]]==2&]