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.
EXAMPLE
The prime indices of 6591 are {2,6,6,6}, for which the only choice is {1,2,3,6}, so 6591 is in the sequence.
The terms together with their prime indices begin:
1: {}
2: {1}
6: {1,2}
9: {2,2}
10: {1,3}
22: {1,5}
25: {3,3}
30: {1,2,3}
34: {1,7}
42: {1,2,4}
45: {2,2,3}
62: {1,11}
63: {2,2,4}
66: {1,2,5}
75: {2,3,3}
82: {1,13}
98: {1,4,4}
99: {2,2,5}
102: {1,2,7}
110: {1,3,5}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Length[Union[Sort /@ Select[Tuples[Divisors/@prix[#]], UnsameQ@@#&]]]==1&]
CROSSREFS
A000005 counts divisors.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2024
STATUS
approved