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

3, 6, 9, 10, 12, 18, 20, 24, 27, 28, 30, 36, 40, 48, 54, 56, 60, 72, 80, 81, 84, 88, 90, 96, 100, 108, 112, 120, 144, 160, 162, 168, 176, 180, 192, 200, 208, 216, 224, 240, 243, 252, 264, 270, 280, 288, 300, 320, 324, 336, 352, 360, 384, 400, 416, 432, 448

Offset: 1

Author

Gus Wiseman, Jul 05 2023

Keywords

• nonn

Comments

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.

Examples

			The terms together with their prime indices begin:
     3: {2}
     6: {1,2}
     9: {2,2}
    10: {1,3}
    12: {1,1,2}
    18: {1,2,2}
    20: {1,1,3}
    24: {1,1,1,2}
    27: {2,2,2}
    28: {1,1,4}
    30: {1,2,3}
    36: {1,1,2,2}
    40: {1,1,1,3}
    48: {1,1,1,1,2}
    54: {1,2,2,2}
    56: {1,1,1,4}
    60: {1,1,2,3}
    72: {1,1,1,2,2}
    80: {1,1,1,1,3}
    81: {2,2,2,2}
		

Crossrefs

For mean 1 we have A000079 except 1.

Partitions of this type are counted by A026905 redoubled.

Equals the complement of A000079 in A344296.

Positions of 2's in A363944 (counted by column 2 of A363946).

For rounded mean 1 we have A363948, counted by A363947.

For rounded-down mean 1 we have A363949, counted by A025065.

The rounded-down or low version is A363954, counted by A363745.

A316413 ranks partitions with integer mean, counted by A067538.

A112798 lists prime indices, length A001222, sum A056239.

A326567/A326568 gives mean of prime indices.

A363941 gives low median of prime indices, triangle A124943.

A363942 gives high median of prime indices, triangle A124944.

Cf. A327473, A327476, A359889, A360005, A360013, A360015, A363727, A363943.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],Ceiling[Mean[prix[#]]]==2&]