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:
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 09 2023
STATUS
approved