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).
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 10 2023
STATUS
approved