A302534 Squarefree numbers whose prime indices are also squarefree and have disjoint prime indices.

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

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