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.
A sequence is gapless if it covers an interval of positive integers.
EXAMPLE
The terms together with their prime indices begin:
1: {}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
15: {2,3}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
35: {3,4}
37: {12}
41: {13}
43: {14}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
nogapQ[m_]:=Or[m=={}, Union[m]==Range[Min[m], Max[m]]];
Select[Range[1, 100, 2], nogapQ[primeMS[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 03 2022
STATUS
approved