A363950 - OEIS

%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