A363954 Numbers whose prime indices have low mean 2.

3, 9, 10, 14, 15, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 70, 75, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 189, 196, 198, 204, 208, 210, 220, 225, 234, 243, 250, 252, 260, 264, 270, 272, 280, 294, 297, 300, 304, 308, 312, 315, 330, 350

Offset: 1

Author

Gus Wiseman, Jul 05 2023

Keywords

• nonn

Comments

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

Examples

			The terms together with their prime indices begin:
     3: {2}
     9: {2,2}
    10: {1,3}
    14: {1,4}
    15: {2,3}
    27: {2,2,2}
    28: {1,1,4}
    30: {1,2,3}
    42: {1,2,4}
    44: {1,1,5}
    45: {2,2,3}
    50: {1,3,3}
    52: {1,1,6}
    63: {2,2,4}
    66: {1,2,5}
    70: {1,3,4}
    75: {2,3,3}
    81: {2,2,2,2}
    84: {1,1,2,4}
    88: {1,1,1,5}
    90: {1,2,2,3}
   100: {1,1,3,3}
		

Crossrefs

Partitions of this type are counted by A363745.

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

For mean 1 we have A363949.

The high version is A363950, counted by A026905.

A112798 lists prime indices, length A001222, sum A056239.

A316413 ranks partitions with integer mean, counted by A067538.

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.

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

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

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],Floor[Mean[prix[#]]]==2&]