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

1,2

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..59.

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}}
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}}

Mathematica

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

Crossrefs

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

Sequence in context: A073328 A119988 A087005 * A240101 A032892 A031941

Adjacent sequences: A302594 A302595 A302596 * A302598 A302599 A302600

Keyword

nonn

Author

Gus Wiseman, Apr 10 2018

Status

approved