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A363948
Numbers whose prime indices have mean < 3/2.
11
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
1,1
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.
EXAMPLE
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
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Mean[prix[#]]<3/2&]
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.
Sequence in context: A363122 A116882 A069519 * A087980 A181818 A363063
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 02 2023
STATUS
approved