A363133 - OEIS

%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