A360252 Numbers for which the prime indices have greater mean than the distinct prime indices.

18, 50, 54, 75, 98, 108, 147, 150, 162, 242, 245, 250, 294, 324, 338, 350, 363, 375, 450, 486, 490, 500, 507, 578, 588, 605, 648, 686, 722, 726, 735, 750, 845, 847, 867, 882, 972, 1014, 1029, 1050, 1058, 1078, 1083, 1125, 1183, 1210, 1250, 1274, 1350, 1372

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:
    18: {1,2,2}
    50: {1,3,3}
    54: {1,2,2,2}
    75: {2,3,3}
    98: {1,4,4}
   108: {1,1,2,2,2}
   147: {2,4,4}
   150: {1,2,3,3}
   162: {1,2,2,2,2}
   242: {1,5,5}
   245: {3,4,4}
   250: {1,3,3,3}
   294: {1,2,4,4}
   324: {1,1,2,2,2,2}
For example, the prime indices of 350 are {1,3,3,4} with mean 11/4, and the distinct prime indices are {1,3,4} with mean 8/3, so 350 is in the sequence.

Mathematica

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

Crossrefs

For unequal instead of greater we have A360246, counted by A360242.

For equal instead of greater we have A360247, counted by A360243.

These partitions are counted by A360250.

For less instead of greater we have A360253, counted by A360251.

A112798 lists prime indices, length A001222, sum A056239.

A316413 lists numbers whose indices have integer mean, distinct A326621.

A326567/A326568 gives mean of prime indices.

A326619/A326620 gives mean of distinct prime indices.

Cf. A000975, A051293, A058398, A067340, A067538, A324570, A327482, A359903, A360005, A360241, A360248.

Sequence in context: A335377 A317258 A071365 * A097319 A258211 A354929

Adjacent sequences: A360249 A360250 A360251 * A360253 A360254 A360255

Keyword

nonn

Author

Gus Wiseman, Feb 09 2023

Status

approved