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Numbers whose prime indices have low mean 2.
3

%I #5 Jul 06 2023 08:55:20

%S 3,9,10,14,15,27,28,30,42,44,45,50,52,63,66,70,75,81,84,88,90,100,104,

%T 126,132,135,136,140,150,152,156,189,196,198,204,208,210,220,225,234,

%U 243,250,252,260,264,270,272,280,294,297,300,304,308,312,315,330,350

%N Numbers whose prime indices have low mean 2.

%C Extending the terminology of A124944, the "low mean" of a multiset is obtained by taking the mean and rounding down.

%e The terms together with their prime indices begin:

%e 3: {2}

%e 9: {2,2}

%e 10: {1,3}

%e 14: {1,4}

%e 15: {2,3}

%e 27: {2,2,2}

%e 28: {1,1,4}

%e 30: {1,2,3}

%e 42: {1,2,4}

%e 44: {1,1,5}

%e 45: {2,2,3}

%e 50: {1,3,3}

%e 52: {1,1,6}

%e 63: {2,2,4}

%e 66: {1,2,5}

%e 70: {1,3,4}

%e 75: {2,3,3}

%e 81: {2,2,2,2}

%e 84: {1,1,2,4}

%e 88: {1,1,1,5}

%e 90: {1,2,2,3}

%e 100: {1,1,3,3}

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[100],Floor[Mean[prix[#]]]==2&]

%Y Partitions of this type are counted by A363745.

%Y Positions of 2's in A363943 (high A363944), triangle A363945 (high A363946).

%Y For mean 1 we have A363949.

%Y The high version is A363950, counted by A026905.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A316413 ranks partitions with integer mean, counted by A067538.

%Y A326567/A326568 gives mean of prime indices.

%Y A363941 gives low median of prime indices, triangle A124943.

%Y A363942 gives high median of prime indices, triangle A124944.

%Y A363948 lists numbers whose prime indices have mean 1, counted by A363947.

%Y Cf. A327473, A327476, A359889, A360013, A360015, A363488, A363951.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jul 05 2023