cp's OEIS Frontend

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

%I A363948 #14 Jul 09 2023 16:27:01
%S A363948 2,4,8,12,16,24,32,48,64,72,80,96,128,144,160,192,256,288,320,384,432,
%T A363948 448,480,512,576,640,768,864,896,960,1024,1152,1280,1536,1728,1792,
%U A363948 1920,2048,2304,2560,2592,2688,2816,2880,3072,3200,3456,3584,3840,4096,4608
%N A363948 Numbers whose prime indices have mean < 3/2.
%C A363948 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.
%e A363948 The initial terms, prime indices, and means:
%e A363948     2: {1} -> 1
%e A363948     4: {1,1} -> 1
%e A363948     8: {1,1,1} -> 1
%e A363948    12: {1,1,2} -> 4/3
%e A363948    16: {1,1,1,1} -> 1
%e A363948    24: {1,1,1,2} -> 5/4
%e A363948    32: {1,1,1,1,1} -> 1
%e A363948    48: {1,1,1,1,2} -> 6/5
%e A363948    64: {1,1,1,1,1,1} -> 1
%e A363948    72: {1,1,1,2,2} -> 7/5
%e A363948    80: {1,1,1,1,3} -> 7/5
%e A363948    96: {1,1,1,1,1,2} -> 7/6
%t A363948 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363948 Select[Range[100],Mean[prix[#]]<3/2&]
%Y A363948 These partitions are counted by A363947.
%Y A363948 Prime indices have mean A326567/A326568.
%Y A363948 For low mode we have A360015, high A360013.
%Y A363948 Positions of 1's in A363489.
%Y A363948 A112798 lists prime indices, length A001222, sum A056239.
%Y A363948 A316413 ranks partitions with integer mean, counted by A067538.
%Y A363948 A360005 gives twice the median of prime indices.
%Y A363948 A363949 ranks partitions with low mean 1, counted by A025065.
%Y A363948 A363950 ranks partitions with low mean 2, counted by A026905 redoubled.
%Y A363948 Cf. A051293, A124944, A327473, A327476, A327482, A359889, A363727, A363942, A363943, A363946, A363951.
%K A363948 nonn
%O A363948 1,1
%A A363948 _Gus Wiseman_, Jul 02 2023