A363948 Numbers whose prime indices have mean < 3/2.

2, 4, 8, 12, 16, 24, 32, 48, 64, 72, 80, 96, 128, 144, 160, 192, 256, 288, 320, 384, 432, 448, 480, 512, 576, 640, 768, 864, 896, 960, 1024, 1152, 1280, 1536, 1728, 1792, 1920, 2048, 2304, 2560, 2592, 2688, 2816, 2880, 3072, 3200, 3456, 3584, 3840, 4096, 4608

Offset: 1

Author

Gus Wiseman, Jul 02 2023

Keywords

• nonn

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The initial terms, prime indices, and means:
    2: {1} -> 1
    4: {1,1} -> 1
    8: {1,1,1} -> 1
   12: {1,1,2} -> 4/3
   16: {1,1,1,1} -> 1
   24: {1,1,1,2} -> 5/4
   32: {1,1,1,1,1} -> 1
   48: {1,1,1,1,2} -> 6/5
   64: {1,1,1,1,1,1} -> 1
   72: {1,1,1,2,2} -> 7/5
   80: {1,1,1,1,3} -> 7/5
   96: {1,1,1,1,1,2} -> 7/6
		

Crossrefs

These partitions are counted by A363947.

Prime indices have mean A326567/A326568.

For low mode we have A360015, high A360013.

Positions of 1's in A363489.

A112798 lists prime indices, length A001222, sum A056239.

A316413 ranks partitions with integer mean, counted by A067538.

A360005 gives twice the median of prime indices.

A363949 ranks partitions with low mean 1, counted by A025065.

A363950 ranks partitions with low mean 2, counted by A026905 redoubled.

Cf. A051293, A124944, A327473, A327476, A327482, A359889, A363727, A363942, A363943, A363946, A363951.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Mean[prix[#]]<3/2&]