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A302534 Squarefree numbers whose prime indices are also squarefree and have disjoint prime indices. 2
1, 2, 3, 5, 6, 10, 11, 13, 15, 17, 22, 26, 29, 30, 31, 33, 34, 41, 43, 47, 51, 55, 58, 59, 62, 66, 67, 73, 79, 82, 83, 85, 86, 93, 94, 101, 102, 109, 110, 113, 118, 123, 127, 134, 137, 139, 141, 143, 145, 146, 149, 155, 157, 158, 163, 165, 166, 167, 170, 177 (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..60.

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}}

13: {{1,2}}

15: {{1},{2}}

17: {{4}}

22: {{},{3}}

26: {{},{1,2}}

29: {{1,3}}

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

31: {{5}}

33: {{1},{3}}

34: {{},{4}}

41: {{6}}

43: {{1,4}}

47: {{2,3}}

51: {{1},{4}}

55: {{2},{3}}

58: {{},{1,3}}

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[100], SquareFreeQ[#]&&UnsameQ@@Join@@primeMS/@primeMS[#]&]

CROSSREFS

Cf. A000009, A000961, A001222, A003963, A005117, A007359, A007716, A051424, A056239, A275024, A279375, A281113, A289509, A294786, A301756, A302242, A302243, A302505, A302521.

Sequence in context: A047447 A094739 A302494 * A063451 A276625 A297571

Adjacent sequences:  A302531 A302532 A302533 * A302535 A302536 A302537

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 09 2018

STATUS

approved

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Last modified January 28 04:11 EST 2022. Contains 350654 sequences. (Running on oeis4.)