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A302521 Odd numbers whose prime indices are squarefree and have disjoint prime indices. Numbers n such that the n-th multiset multisystem is a set partition. 5
1, 3, 5, 11, 13, 15, 17, 29, 31, 33, 41, 43, 47, 51, 55, 59, 67, 73, 79, 83, 85, 93, 101, 109, 113, 123, 127, 137, 139, 141, 143, 145, 149, 155, 157, 163, 165, 167, 177, 179, 181, 187, 191, 199, 201, 205, 211, 215, 219, 221, 233, 241, 249, 255, 257, 269, 271 (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..57.

EXAMPLE

Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set partitions.

01: {}

03: {{1}}

05: {{2}}

11: {{3}}

13: {{1,2}}

15: {{1},{2}}

17: {{4}}

29: {{1,3}}

31: {{5}}

33: {{1},{3}}

41: {{6}}

43: {{1,4}}

47: {{2,3}}

51: {{1},{4}}

55: {{2},{3}}

59: {{7}}

67: {{8}}

73: {{2,4}}

79: {{1,5}}

83: {{9}}

85: {{2},{4}}

93: {{1},{5}}

MATHEMATICA

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

Select[Range[1, 100, 2], UnsameQ@@Join@@primeMS/@primeMS[#]&]

CROSSREFS

Cf. A000110, A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279790, A281113, A294788, A301750, A302242, A302243, A302505.

Sequence in context: A284795 A329629 A340019 * A270699 A260398 A065396

Adjacent sequences:  A302518 A302519 A302520 * A302522 A302523 A302524

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 09 2018

STATUS

approved

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Last modified October 27 05:20 EDT 2021. Contains 348271 sequences. (Running on oeis4.)