

A302534


Squarefree numbers whose prime indices are also squarefree and have disjoint prime indices.


2



1, 2, 3, 5, 6, 10, 11, 13, 15, 17, 22, 26, 29, 30, 31, 33, 34, 41, 43, 47, 51, 55, 58, 59, 62, 66, 67, 73, 79, 82, 83, 85, 86, 93, 94, 101, 102, 109, 110, 113, 118, 123, 127, 134, 137, 139, 141, 143, 145, 146, 149, 155, 157, 158, 163, 165, 166, 167, 170, 177
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

A prime index of n is a number m such that prime(m) divides n.


LINKS

Table of n, a(n) for n=1..60.


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}}
05: {{2}}
06: {{},{1}}
10: {{},{2}}
11: {{3}}
13: {{1,2}}
15: {{1},{2}}
17: {{4}}
22: {{},{3}}
26: {{},{1,2}}
29: {{1,3}}
30: {{},{1},{2}}
31: {{5}}
33: {{1},{3}}
34: {{},{4}}
41: {{6}}
43: {{1,4}}
47: {{2,3}}
51: {{1},{4}}
55: {{2},{3}}
58: {{},{1,3}}
59: {{7}}
62: {{},{5}}
66: {{},{1},{3}}


MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], SquareFreeQ[#]&&UnsameQ@@Join@@primeMS/@primeMS[#]&]


CROSSREFS

Cf. A000009, A000961, A001222, A003963, A005117, A007359, A007716, A051424, A056239, A275024, A279375, A281113, A289509, A294786, A301756, A302242, A302243, A302505, A302521.
Sequence in context: A047447 A094739 A302494 * A063451 A276625 A297571
Adjacent sequences: A302531 A302532 A302533 * A302535 A302536 A302537


KEYWORD

nonn


AUTHOR

Gus Wiseman, Apr 09 2018


STATUS

approved



