login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319118 Number of multimin tree-factorizations of n. 3
1, 1, 1, 2, 1, 2, 1, 6, 2, 2, 1, 8, 1, 2, 2, 24, 1, 6, 1, 8, 2, 2, 1, 42, 2, 2, 6, 8, 1, 8, 1, 112, 2, 2, 2, 38, 1, 2, 2, 42, 1, 8, 1, 8, 8, 2, 1, 244, 2, 6, 2, 8, 1, 24, 2, 42, 2, 2, 1, 58, 1, 2, 8, 568, 2, 8, 1, 8, 2, 8, 1, 268, 1, 2, 6, 8, 2, 8, 1, 244, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A multimin factorization of n is an ordered factorization of n into factors greater than 1 such that the sequence of minimal primes dividing each factor is weakly increasing. A multimin tree-factorization of n is either the number n itself or a sequence of multimin tree-factorizations, one of each factor in a multimin factorization of n with at least two factors.

LINKS

Table of n, a(n) for n=1..81.

FORMULA

a(prime^n) = A118376(n).

a(product of n distinct primes) = A005804(n).

EXAMPLE

The a(12) = 8 multimin tree-factorizations:

12,

(2*6), (4*3), (6*2), (2*2*3),

(2*(2*3)), ((2*2)*3), ((2*3)*2).

Or as series-reduced plane trees of multisets:

112,

(1,12), (11,2), (12,1), (1,1,2),

(1,(1,2)), ((1,1),2)), ((1,2),1).

MATHEMATICA

facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]];

mmftrees[n_]:=Prepend[Join@@(Tuples[mmftrees/@#]&/@Select[Join@@Permutations/@Select[facs[n], Length[#]>1&], OrderedQ[FactorInteger[#][[1, 1]]&/@#]&]), n];

Table[Length[mmftrees[n]], {n, 100}]

CROSSREFS

Cf. A001055, A005804, A020639, A118376, A196545, A255397, A281113, A281118, A281119, A295279, A317545, A317546, A318577, A319119.

Sequence in context: A205405 A112623 A130675 * A163820 A284465 A327899

Adjacent sequences: A319115 A319116 A319117 * A319119 A319120 A319121

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 10 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 11:27 EST 2023. Contains 359922 sequences. (Running on oeis4.)