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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326334 Number of sortable factorizations of n. 2
 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 5, 1, 4, 1, 4, 2, 2, 1, 7, 2, 2, 3, 4, 1, 4, 1, 7, 2, 2, 2, 8, 1, 2, 2, 7, 1, 4, 1, 4, 4, 2, 1, 12, 2, 4, 2, 4, 1, 7, 2, 7, 2, 2, 1, 8, 1, 2, 4, 11, 2, 4, 1, 4, 2, 4, 1, 14, 1, 2, 4, 4, 2, 4, 1, 12, 5, 2, 1, 8, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A factorization into factors > 1 is sortable if there is a permutation (c_1,...,c_k) of the factors such that the maximum prime factor (in the standard factorization of an integer into prime numbers) of c_i is at most the minimum prime factor of c_{i+1}. For example, the factorization (6*8*27) is sortable because the permutation (8,6,27) satisfies the condition. LINKS Table of n, a(n) for n=1..86. FORMULA A001055(n) = a(n) + A326291(n). EXAMPLE The a(180) = 16 sortable factorizations: (2*2*3*3*5) (2*2*5*9) (4*5*9) (2*90) (180) (2*3*5*6) (2*2*45) (4*45) (3*3*4*5) (2*5*18) (5*36) (2*2*3*15) (2*6*15) (12*15) (3*4*15) (3*5*12) Missing from this list are the following unsortable factorizations: (2*3*3*10) (5*6*6) (3*60) (2*3*30) (6*30) (2*9*10) (9*20) (3*3*20) (10*18) (3*6*10) MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Select[facs[n], OrderedQ[Join@@Sort[First/@FactorInteger[#]&/@#, OrderedQ[PadRight[{#1, #2}]]&]]&]], {n, 100}] CROSSREFS Factorizations are A001055. Unsortable factorizations are A326291. Sortable integer partitions are A326333. Cf. A058681, A326211, A326212, A326237, A326258, A326332. Sequence in context: A317141 A317791 A318559 * A218320 A355030 A305254 Adjacent sequences: A326331 A326332 A326333 * A326335 A326336 A326337 KEYWORD nonn AUTHOR Gus Wiseman, Jun 27 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 11 19:17 EDT 2024. Contains 375073 sequences. (Running on oeis4.)