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A302597 Squarefree numbers whose prime indices are powers of a common prime number. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)