cp's OEIS Frontend

A363950 Numbers whose prime indices have rounded-up mean 2.

%I A363950 #6 Jul 06 2023 08:56:01
%S A363950 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 A363950 100,108,112,120,144,160,162,168,176,180,192,200,208,216,224,240,243,
%U A363950 252,264,270,280,288,300,320,324,336,352,360,384,400,416,432,448
%N A363950 Numbers whose prime indices have rounded-up mean 2.
%C A363950 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 A363950 The terms together with their prime indices begin:
%e A363950      3: {2}
%e A363950      6: {1,2}
%e A363950      9: {2,2}
%e A363950     10: {1,3}
%e A363950     12: {1,1,2}
%e A363950     18: {1,2,2}
%e A363950     20: {1,1,3}
%e A363950     24: {1,1,1,2}
%e A363950     27: {2,2,2}
%e A363950     28: {1,1,4}
%e A363950     30: {1,2,3}
%e A363950     36: {1,1,2,2}
%e A363950     40: {1,1,1,3}
%e A363950     48: {1,1,1,1,2}
%e A363950     54: {1,2,2,2}
%e A363950     56: {1,1,1,4}
%e A363950     60: {1,1,2,3}
%e A363950     72: {1,1,1,2,2}
%e A363950     80: {1,1,1,1,3}
%e A363950     81: {2,2,2,2}
%t A363950 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363950 Select[Range[1000],Ceiling[Mean[prix[#]]]==2&]
%Y A363950 For mean 1 we have A000079 except 1.
%Y A363950 Partitions of this type are counted by A026905 redoubled.
%Y A363950 Equals the complement of A000079 in A344296.
%Y A363950 Positions of 2's in A363944 (counted by column 2 of A363946).
%Y A363950 For rounded mean 1 we have A363948, counted by A363947.
%Y A363950 For rounded-down mean 1 we have A363949, counted by A025065.
%Y A363950 The rounded-down or low version is A363954, counted by A363745.
%Y A363950 A316413 ranks partitions with integer mean, counted by A067538.
%Y A363950 A112798 lists prime indices, length A001222, sum A056239.
%Y A363950 A326567/A326568 gives mean of prime indices.
%Y A363950 A363941 gives low median of prime indices, triangle A124943.
%Y A363950 A363942 gives high median of prime indices, triangle A124944.
%Y A363950 Cf. A327473, A327476, A359889, A360005, A360013, A360015, A363727, A363943.
%K A363950 nonn
%O A363950 1,1
%A A363950 _Gus Wiseman_, Jul 05 2023