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A302539 Squarefree numbers whose prime indices other than 1 are prime numbers. 2
1, 2, 3, 5, 6, 10, 11, 15, 17, 22, 30, 31, 33, 34, 41, 51, 55, 59, 62, 66, 67, 82, 83, 85, 93, 102, 109, 110, 118, 123, 127, 134, 155, 157, 165, 166, 170, 177, 179, 186, 187, 191, 201, 205, 211, 218, 241, 246, 249, 254, 255, 277, 283, 295, 310, 314, 327, 330 (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

Andrew Howroyd, 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}}

05: {{2}}

06: {{},{1}}

10: {{},{2}}

11: {{3}}

15: {{1},{2}}

17: {{4}}

22: {{},{3}}

30: {{},{1},{2}}

31: {{5}}

33: {{1},{3}}

34: {{},{4}}

41: {{6}}

51: {{1},{4}}

55: {{2},{3}}

59: {{7}}

62: {{},{5}}

66: {{},{1},{3}}

MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[400], SquareFreeQ[#]&&And@@(PrimeQ/@DeleteCases[primeMS[#], 1])&]

PROG

(PARI) ok(n)={issquarefree(n) && !#select(p->p>2 && !isprime(primepi(p)), factor(n)[, 1])} \\ Andrew Howroyd, Aug 26 2018

CROSSREFS

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A076610, A275024, A281113, A302242, A302243, A302534.

Sequence in context: A255059 A057760 A074243 * A322912 A072720 A298363

Adjacent sequences:  A302536 A302537 A302538 * A302540 A302541 A302542

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 09 2018

STATUS

approved

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)