A302521 Odd numbers whose prime indices are squarefree and have disjoint prime indices. Numbers n such that the n-th multiset multisystem is a set partition.

1, 3, 5, 11, 13, 15, 17, 29, 31, 33, 41, 43, 47, 51, 55, 59, 67, 73, 79, 83, 85, 93, 101, 109, 113, 123, 127, 137, 139, 141, 143, 145, 149, 155, 157, 163, 165, 167, 177, 179, 181, 187, 191, 199, 201, 205, 211, 215, 219, 221, 233, 241, 249, 255, 257, 269, 271

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..57.

Example

Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set partitions.
01: {}
03: {{1}}
05: {{2}}
11: {{3}}
13: {{1,2}}
15: {{1},{2}}
17: {{4}}
29: {{1,3}}
31: {{5}}
33: {{1},{3}}
41: {{6}}
43: {{1,4}}
47: {{2,3}}
51: {{1},{4}}
55: {{2},{3}}
59: {{7}}
67: {{8}}
73: {{2,4}}
79: {{1,5}}
83: {{9}}
85: {{2},{4}}
93: {{1},{5}}

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1, 100, 2], UnsameQ@@Join@@primeMS/@primeMS[#]&]

Crossrefs

Cf. A000110, A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279790, A281113, A294788, A301750, A302242, A302243, A302505.

Sequence in context: A284795 A329629 A340019 * A270699 A260398 A065396

Adjacent sequences: A302518 A302519 A302520 * A302522 A302523 A302524

Keyword

nonn

Author

Gus Wiseman, Apr 09 2018

Status

approved