login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320456 Numbers whose multiset multisystem spans an initial interval of positive integers. 34
1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 19, 21, 24, 26, 27, 28, 30, 32, 35, 36, 37, 38, 39, 42, 45, 48, 49, 52, 53, 54, 56, 57, 60, 61, 63, 64, 65, 69, 70, 72, 74, 75, 76, 78, 81, 84, 89, 90, 91, 95, 96, 98, 104, 105, 106, 108, 111, 112, 113, 114, 117 (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. The multiset of prime indices of n is row n of A112798. The n-th multiset multisystem is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the 78th multiset multisystem is {{},{1},{1,2}}.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

The sequence of terms together with their multiset multisystems begins:

   1: {}

   2: {{}}

   3: {{1}}

   4: {{},{}}

   6: {{},{1}}

   7: {{1,1}}

   8: {{},{},{}}

   9: {{1},{1}}

  12: {{},{},{1}}

  13: {{1,2}}

  14: {{},{1,1}}

  15: {{1},{2}}

  16: {{},{},{},{}}

  18: {{},{1},{1}}

  19: {{1,1,1}}

  21: {{1},{1,1}}

  24: {{},{},{},{1}}

  26: {{},{1,2}}

  27: {{1},{1},{1}}

  28: {{},{},{1,1}}

  30: {{},{1},{2}}

  32: {{},{},{},{},{}}

MATHEMATICA

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

normQ[sys_]:=Or[Length[sys]==0, Union@@sys==Range[Max@@Max@@sys]];

Select[Range[100], normQ[primeMS/@primeMS[#]]&]

CROSSREFS

Cf. A001222, A003963, A034691, A034729, A055932, A056239, A112798, A255906, A290103, A302242, A305052.

Cf. A320458, A320459, A320461, A320462, A320463, A320464, A320532, A320533.

Sequence in context: A059325 A258938 A004763 * A330060 A330108 A330104

Adjacent sequences:  A320453 A320454 A320455 * A320457 A320458 A320459

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 13 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 9 09:40 EDT 2020. Contains 335542 sequences. (Running on oeis4.)