cp's OEIS Frontend

A360252 Numbers for which the prime indices have greater mean than the distinct prime indices.

%I A360252 #5 Feb 10 2023 14:29:35
%S A360252 18,50,54,75,98,108,147,150,162,242,245,250,294,324,338,350,363,375,
%T A360252 450,486,490,500,507,578,588,605,648,686,722,726,735,750,845,847,867,
%U A360252 882,972,1014,1029,1050,1058,1078,1083,1125,1183,1210,1250,1274,1350,1372
%N A360252 Numbers for which the prime indices have greater mean than the distinct prime indices.
%C A360252 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 A360252 The terms together with their prime indices begin:
%e A360252     18: {1,2,2}
%e A360252     50: {1,3,3}
%e A360252     54: {1,2,2,2}
%e A360252     75: {2,3,3}
%e A360252     98: {1,4,4}
%e A360252    108: {1,1,2,2,2}
%e A360252    147: {2,4,4}
%e A360252    150: {1,2,3,3}
%e A360252    162: {1,2,2,2,2}
%e A360252    242: {1,5,5}
%e A360252    245: {3,4,4}
%e A360252    250: {1,3,3,3}
%e A360252    294: {1,2,4,4}
%e A360252    324: {1,1,2,2,2,2}
%e A360252 For example, the prime indices of 350 are {1,3,3,4} with mean 11/4, and the distinct prime indices are {1,3,4} with mean 8/3, so 350 is in the sequence.
%t A360252 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360252 Select[Range[100],Mean[prix[#]]>Mean[Union[prix[#]]]&]
%Y A360252 For unequal instead of greater we have A360246, counted by A360242.
%Y A360252 For equal instead of greater we have A360247, counted by A360243.
%Y A360252 These partitions are counted by A360250.
%Y A360252 For less instead of greater we have A360253, counted by A360251.
%Y A360252 A112798 lists prime indices, length A001222, sum A056239.
%Y A360252 A316413 lists numbers whose indices have integer mean, distinct A326621.
%Y A360252 A326567/A326568 gives mean of prime indices.
%Y A360252 A326619/A326620 gives mean of distinct prime indices.
%Y A360252 Cf. A000975, A051293, A058398, A067340, A067538, A324570, A327482, A359903, A360005, A360241, A360248.
%K A360252 nonn
%O A360252 1,1
%A A360252 _Gus Wiseman_, Feb 09 2023