OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set systems.
01: {}
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
06: {{},{1}}
07: {{1,1}}
08: {{},{},{}}
09: {{1},{1}}
10: {{},{2}}
11: {{3}}
12: {{},{},{1}}
14: {{},{1,1}}
16: {{},{},{},{}}
17: {{4}}
18: {{},{1},{1}}
19: {{1,1,1}}
20: {{},{},{2}}
21: {{1},{1,1}}
22: {{},{3}}
23: {{2,2}}
24: {{},{},{},{1}}
25: {{2},{2}}
27: {{1},{1},{1}}
28: {{},{},{1,1}}
31: {{5}}
32: {{},{},{},{},{}}
34: {{},{4}}
36: {{},{},{1},{1}}
38: {{},{1,1,1}}
40: {{},{},{},{2}}
MAPLE
filter:= proc(n) local F, q;
uses numtheory;
F:= map(pi, factorset(n));
nops(`union`(op(map(factorset, F)))) <= 1
end proc:
select(filter, [$1..200]); # Robert Israel, Oct 22 2020
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], SameQ@@Join@@primeMS/@primeMS[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2018
STATUS
approved