cp's OEIS Frontend

A360253 Numbers for which the prime indices have lesser mean than the distinct prime indices.

%I A360253 #7 Feb 10 2023 14:29:29
%S A360253 12,20,24,28,40,44,45,48,52,56,60,63,68,72,76,80,84,88,92,96,99,104,
%T A360253 112,116,117,120,124,126,132,135,136,140,144,148,152,153,156,160,164,
%U A360253 168,171,172,175,176,180,184,188,189,192,198,200,204,207,208,212,220
%N A360253 Numbers for which the prime indices have lesser mean than the distinct prime indices.
%C A360253 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 A360253 The terms together with their prime indices begin:
%e A360253    12: {1,1,2}
%e A360253    20: {1,1,3}
%e A360253    24: {1,1,1,2}
%e A360253    28: {1,1,4}
%e A360253    40: {1,1,1,3}
%e A360253    44: {1,1,5}
%e A360253    45: {2,2,3}
%e A360253    48: {1,1,1,1,2}
%e A360253    52: {1,1,6}
%e A360253    56: {1,1,1,4}
%e A360253    60: {1,1,2,3}
%e A360253    63: {2,2,4}
%e A360253    68: {1,1,7}
%e A360253    72: {1,1,1,2,2}
%e A360253 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 not in the sequence.
%t A360253 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360253 Select[Range[100],Mean[prix[#]]<Mean[Union[prix[#]]]&]
%Y A360253 These partitions are counted by A360251.
%Y A360253 For unequal instead of less we have A360246, counted by A360242.
%Y A360253 For equal instead of less we have A360247, counted by A360243.
%Y A360253 For greater instead of less we have A360252, counted by A360250.
%Y A360253 A112798 lists prime indices, length A001222, sum A056239.
%Y A360253 A316413 lists numbers whose indices have integer mean, distinct A326621.
%Y A360253 A326567/A326568 gives mean of prime indices.
%Y A360253 A326619/A326620 gives mean of distinct prime indices.
%Y A360253 Cf. A000975, A051293, A058398, A067340, A067538, A324570, A327482, A359903, A360005, A360241, A360248.
%K A360253 nonn
%O A360253 1,1
%A A360253 _Gus Wiseman_, Feb 09 2023