A302594 - OEIS

A302594

Numbers whose prime indices other than 1 are equal prime numbers.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 16, 17, 18, 20, 22, 24, 25, 27, 31, 32, 34, 36, 40, 41, 44, 48, 50, 54, 59, 62, 64, 67, 68, 72, 80, 81, 82, 83, 88, 96, 100, 108, 109, 118, 121, 124, 125, 127, 128, 134, 136, 144, 157, 160, 162, 164, 166, 176, 179, 191, 192

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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..62.

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}}

04: {{},{}}

05: {{2}}

06: {{},{1}}

08: {{},{},{}}

09: {{1},{1}}

10: {{},{2}}

11: {{3}}

12: {{},{},{1}}

16: {{},{},{},{}}

17: {{4}}

18: {{},{1},{1}}

20: {{},{},{2}}

22: {{},{3}}

24: {{},{},{},{1}}

MATHEMATICA

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

Select[Range[400], MatchQ[Union[DeleteCases[primeMS[#], 1]], {_?PrimeQ}|{}]&]

CROSSREFS

Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A047968, A281113, A295924, A301760, A302242, A302243.

Sequence in context: A277620 A031143 A358521 * A055492 A005459 A039216

Adjacent sequences: A302591 A302592 A302593 * A302595 A302596 A302597

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 10 2018

STATUS

approved