A302505 Numbers whose prime indices are squarefree and have disjoint prime indices.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 16, 17, 20, 22, 24, 26, 29, 30, 31, 32, 33, 34, 40, 41, 43, 44, 47, 48, 51, 52, 55, 58, 59, 60, 62, 64, 66, 67, 68, 73, 79, 80, 82, 83, 85, 86, 88, 93, 94, 96, 101, 102, 104, 109, 110, 113, 116, 118, 120, 123, 124, 127

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..64.

Example

Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
01: {}
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
06: {{},{1}}
08: {{},{},{}}
10: {{},{2}}
11: {{3}}
12: {{},{},{1}}
13: {{1,2}}
15: {{1},{2}}
16: {{},{},{},{}}
17: {{4}}
20: {{},{},{2}}
22: {{},{3}}
24: {{},{},{},{1}}
26: {{},{1,2}}
29: {{1,3}}
30: {{},{1},{2}}
31: {{5}}
32: {{},{},{},{},{}}

Mathematica

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

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279790, A281113, A294788, A301750, A302242, A302243.

Sequence in context: A047424 A094942 A243494 * A102705 A180636 A182625

Adjacent sequences: A302502 A302503 A302504 * A302506 A302507 A302508

Keyword

nonn

Author

Gus Wiseman, Apr 09 2018

Status

approved