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:
1: {}
10: {1,3}
39: {2,6}
68: {1,1,7}
115: {3,9}
138: {1,2,9}
259: {4,12}
310: {1,3,11}
328: {1,1,1,13}
387: {2,2,14}
517: {5,15}
574: {1,4,13}
636: {1,1,2,16}
For example, the prime indices of 138 are {1,2,9}, with mean 4, and with first differences (1,7), with mean also 4, so 138 is in the sequence.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 1000], Mean[prix[#]]==Mean[Differences[prix[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 18 2023
STATUS
approved