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.
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:
2: {1}
3: {2}
5: {3}
7: {4}
8: {1,1,1}
11: {5}
13: {6}
17: {7}
19: {8}
23: {9}
27: {2,2,2}
29: {10}
30: {1,2,3}
31: {11}
32: {1,1,1,1,1}
For example, the prime indices of 180 are {1,1,2,2,3}, with mean 9/5 and median 2, so 180 is not in the sequence.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], OddQ[PrimeOmega[#]]&&Mean[prix[#]]==Median[prix[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 22 2023
STATUS
approved