A363133 Numbers > 1 whose prime indices satisfy 2*(minimum) = (mean).

10, 28, 30, 39, 84, 88, 90, 100, 115, 171, 208, 252, 255, 259, 264, 270, 273, 280, 300, 363, 517, 544, 624, 756, 783, 784, 792, 793, 810, 840, 880, 900, 925, 1000, 1035, 1085, 1197, 1216, 1241, 1425, 1495, 1521, 1595, 1615, 1632, 1683, 1691, 1785, 1872, 1911

Offset: 1

Author

Gus Wiseman, May 29 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:
    10: {1,3}
    28: {1,1,4}
    30: {1,2,3}
    39: {2,6}
    84: {1,1,2,4}
    88: {1,1,1,5}
    90: {1,2,2,3}
   100: {1,1,3,3}
   115: {3,9}
   171: {2,2,8}
   208: {1,1,1,1,6}
   252: {1,1,2,2,4}
   255: {2,3,7}
   259: {4,12}
   264: {1,1,1,2,5}
		

Crossrefs

Removing the factor 2 gives A000961.

For maximum instead of mean we have A361908, counted by A118096.

Partitions of this type are counted by A363132.

For length instead of mean we have A363134, counted by A237757.

For 2*(maximum) = (length) we have A363218, counted by A237753.

A051293 counts subsets with integer mean.

A112798 lists prime indices, length A001222, sum A056239.

A360005 gives twice median of prime indices.

Cf. A006141, A106529, A111907, A237755, A237824, A324522, A327482, A361860, A361861, A362050.

Programs

Mathematica

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