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

1,1

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.

Links

Table of n, a(n) for n=1..50.

Example

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}

Mathematica

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

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.

Sequence in context: A196359 A184686 A251326 * A022422 A113962 A031105

Adjacent sequences: A363130 A363131 A363132 * A363134 A363135 A363136

Keyword

nonn

Author

Gus Wiseman, May 29 2023

Status

approved