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!)
A326257 MM-numbers of weakly nesting multiset partitions. 11
49, 91, 98, 133, 147, 169, 182, 196, 203, 245, 247, 259, 266, 273, 294, 299, 301, 338, 343, 361, 364, 371, 377, 392, 399, 406, 427, 441, 455, 481, 490, 494, 497, 507, 518, 529, 532, 539, 546, 551, 553, 559, 588, 598, 602, 609, 623, 637, 665, 667, 676, 686, 689 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 multiset multisystem with MM-number n is obtained by taking the multiset of prime indices of each prime index of n.

A multiset partition is weakly nesting if it has two blocks of the form {...x,y...}, {...z,t...} where x <= z and t <= y or z <= x and y <= t.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

The sequence of terms together with their multiset multisystems begins:

   49: {{1,1},{1,1}}

   91: {{1,1},{1,2}}

   98: {{},{1,1},{1,1}}

  133: {{1,1},{1,1,1}}

  147: {{1},{1,1},{1,1}}

  169: {{1,2},{1,2}}

  182: {{},{1,1},{1,2}}

  196: {{},{},{1,1},{1,1}}

  203: {{1,1},{1,3}}

  245: {{2},{1,1},{1,1}}

  247: {{1,2},{1,1,1}}

  259: {{1,1},{1,1,2}}

  266: {{},{1,1},{1,1,1}}

  273: {{1},{1,1},{1,2}}

  294: {{},{1},{1,1},{1,1}}

  299: {{1,2},{2,2}}

  301: {{1,1},{1,4}}

  338: {{},{1,2},{1,2}}

  343: {{1,1},{1,1},{1,1}}

  361: {{1,1,1},{1,1,1}}

MATHEMATICA

wknXQ[stn_]:=MatchQ[stn, {___, {___, x_, y_, ___}, ___, {___, z_, t_, ___}, ___}/; (x<=z&&y>=t)||(x>=z&&y<=t)]

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

Select[Range[1000], wknXQ[primeMS/@primeMS[#]]&]

CROSSREFS

MM-numbers of crossing multiset partitions are A324170.

MM-numbers of nesting multiset partitions are A324256.

MM-numbers of capturing multiset partitions are A326255.

Nesting set partitions are A016098.

Cf. A001055, A034827, A056239, A112798, A122880, A302242, A324171.

Cf. A326211, A326243, A326258, A326260.

Sequence in context: A093894 A259766 A273937 * A231275 A158725 A090825

Adjacent sequences:  A326254 A326255 A326256 * A326258 A326259 A326260

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 21 2019

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 June 22 12:56 EDT 2021. Contains 345380 sequences. (Running on oeis4.)