|
|
A360453
|
|
Numbers for which the prime multiplicities (or sorted signature) have the same median as the distinct prime indices.
|
|
12
|
|
|
1, 2, 9, 12, 18, 40, 100, 112, 125, 180, 250, 252, 300, 352, 360, 392, 396, 405, 450, 468, 504, 540, 588, 600, 612, 675, 684, 720, 756, 792, 828, 832, 882, 900, 936, 1008, 1044, 1116, 1125, 1176, 1188, 1200, 1224, 1332, 1350, 1368, 1372, 1404, 1440, 1452, 1476
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
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.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
|
|
LINKS
|
|
|
EXAMPLE
|
The terms together with their prime indices begin:
1: {}
2: {1}
9: {2,2}
12: {1,1,2}
18: {1,2,2}
40: {1,1,1,3}
100: {1,1,3,3}
112: {1,1,1,1,4}
125: {3,3,3}
180: {1,1,2,2,3}
250: {1,3,3,3}
252: {1,1,2,2,4}
300: {1,1,2,3,3}
352: {1,1,1,1,1,5}
360: {1,1,1,2,2,3}
For example, the prime indices of 756 are {1,1,2,2,2,4} with distinct parts {1,2,4} with median 2 and multiplicities {1,2,3} with median 2, so 756 is in the sequence.
|
|
MATHEMATICA
|
Select[Range[100], #==1||Median[Last/@FactorInteger[#]]== Median[PrimePi/@First/@FactorInteger[#]]&]
|
|
CROSSREFS
|
For indices instead of multiplicities we have A360249, counted by A360245.
For indices instead of distinct indices we have A360454, counted by A360456.
These partitions are counted by A360455.
A316413 = numbers whose prime indices have integer mean, distinct A326621.
A360005 gives median of prime indices (times two).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|