A302593 Numbers whose prime indices are powers of a common prime number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 31, 32, 34, 36, 38, 40, 41, 42, 44, 46, 48, 49, 50, 53, 54, 56, 57, 59, 62, 63, 64, 67, 68, 72, 76, 80, 81, 82, 83, 84, 88, 92, 96, 97, 98, 100, 103, 106, 108, 109, 112

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

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A047968, A281113, A295924, A301760, A302242, A302243.

Sequence in context: A172974 A066255 A330236 * A129304 A337149 A294358

Adjacent sequences: A302590 A302591 A302592 * A302594 A302595 A302596

Keyword

nonn

Author

Gus Wiseman, Apr 10 2018

Status

approved