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%I #6 Jul 06 2023 08:56:01
%S 3,6,9,10,12,18,20,24,27,28,30,36,40,48,54,56,60,72,80,81,84,88,90,96,
%T 100,108,112,120,144,160,162,168,176,180,192,200,208,216,224,240,243,
%U 252,264,270,280,288,300,320,324,336,352,360,384,400,416,432,448
%N Numbers whose prime indices have rounded-up mean 2.
%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 3: {2}
%e 6: {1,2}
%e 9: {2,2}
%e 10: {1,3}
%e 12: {1,1,2}
%e 18: {1,2,2}
%e 20: {1,1,3}
%e 24: {1,1,1,2}
%e 27: {2,2,2}
%e 28: {1,1,4}
%e 30: {1,2,3}
%e 36: {1,1,2,2}
%e 40: {1,1,1,3}
%e 48: {1,1,1,1,2}
%e 54: {1,2,2,2}
%e 56: {1,1,1,4}
%e 60: {1,1,2,3}
%e 72: {1,1,1,2,2}
%e 80: {1,1,1,1,3}
%e 81: {2,2,2,2}
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[1000],Ceiling[Mean[prix[#]]]==2&]
%Y For mean 1 we have A000079 except 1.
%Y Partitions of this type are counted by A026905 redoubled.
%Y Equals the complement of A000079 in A344296.
%Y Positions of 2's in A363944 (counted by column 2 of A363946).
%Y For rounded mean 1 we have A363948, counted by A363947.
%Y For rounded-down mean 1 we have A363949, counted by A025065.
%Y The rounded-down or low version is A363954, counted by A363745.
%Y A316413 ranks partitions with integer mean, counted by A067538.
%Y A112798 lists prime indices, length A001222, sum A056239.
%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 Cf. A327473, A327476, A359889, A360005, A360013, A360015, A363727, A363943.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 05 2023