login
A363133
Numbers > 1 whose prime indices satisfy 2*(minimum) = (mean).
2
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.
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.
Sequence in context: A196359 A184686 A251326 * A022422 A113962 A031105
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 29 2023
STATUS
approved