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:
12: {1,1,2}
20: {1,1,3}
24: {1,1,1,2}
28: {1,1,4}
40: {1,1,1,3}
44: {1,1,5}
45: {2,2,3}
48: {1,1,1,1,2}
52: {1,1,6}
56: {1,1,1,4}
60: {1,1,2,3}
63: {2,2,4}
68: {1,1,7}
72: {1,1,1,2,2}
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 not 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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 09 2023
STATUS
approved