A302597 Squarefree numbers whose prime indices are powers of a common prime number.

1, 2, 3, 5, 6, 7, 10, 11, 14, 17, 19, 21, 22, 23, 31, 34, 38, 41, 42, 46, 53, 57, 59, 62, 67, 82, 83, 97, 103, 106, 109, 114, 115, 118, 127, 131, 133, 134, 157, 159, 166, 179, 191, 194, 206, 211, 218, 227, 230, 241, 254, 262, 266, 277, 283, 311, 314, 318, 331

Offset: 1

Author

Gus Wiseman, Apr 10 2018

Keywords

• nonn

Comments

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

Examples

			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}}
07: {{1,1}}
10: {{},{2}}
11: {{3}}
14: {{},{1,1}}
17: {{4}}
19: {{1,1,1}}
21: {{1},{1,1}}
22: {{},{3}}
23: {{2,2}}
31: {{5}}
34: {{},{4}}
38: {{},{1,1,1}}
		

Crossrefs

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A047966, A281113, A296134, A301766, A302242, A302243.

Programs

Mathematica

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