|
%I #6 May 31 2023 10:48:35
%S 10,28,30,39,84,88,90,100,115,171,208,252,255,259,264,270,273,280,300,
%T 363,517,544,624,756,783,784,792,793,810,840,880,900,925,1000,1035,
%U 1085,1197,1216,1241,1425,1495,1521,1595,1615,1632,1683,1691,1785,1872,1911
%N Numbers > 1 whose prime indices satisfy 2*(minimum) = (mean).
%C 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 The terms together with their prime indices begin:
%e 10: {1,3}
%e 28: {1,1,4}
%e 30: {1,2,3}
%e 39: {2,6}
%e 84: {1,1,2,4}
%e 88: {1,1,1,5}
%e 90: {1,2,2,3}
%e 100: {1,1,3,3}
%e 115: {3,9}
%e 171: {2,2,8}
%e 208: {1,1,1,1,6}
%e 252: {1,1,2,2,4}
%e 255: {2,3,7}
%e 259: {4,12}
%e 264: {1,1,1,2,5}
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],Mean[prix[#]]==2*Min[prix[#]]&]
%Y Removing the factor 2 gives A000961.
%Y For maximum instead of mean we have A361908, counted by A118096.
%Y Partitions of this type are counted by A363132.
%Y For length instead of mean we have A363134, counted by A237757.
%Y For 2*(maximum) = (length) we have A363218, counted by A237753.
%Y A051293 counts subsets with integer mean.
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A360005 gives twice median of prime indices.
%Y Cf. A006141, A106529, A111907, A237755, A237824, A324522, A327482, A361860, A361861, A362050.
%K nonn
%O 1,1
%A _Gus Wiseman_, May 29 2023
|
