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

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325989 Number of perfect factorizations of n. 2
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS A perfect factorization of n is an orderless factorization of n into factors > 1 such that every divisor of n is the product of exactly one submultiset of the factors. This is the intersection of covering (or complete) factorizations (A325988) and knapsack factorizations (A292886). LINKS FORMULA a(2^n) = A002033(n). EXAMPLE The a(216) = 4 perfect factorizations:   (2*2*2*3*3*3)   (2*2*2*3*9)   (2*3*3*3*4)   (2*3*4*9) 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], Sort[Times@@@Union[Subsets[#]]]==Divisors[n]&]], {n, 100}] CROSSREFS Positions of terms > 1 are A325990. Cf. A002033, A103300, A292886, A325685, A325780, A325787, A325789, A325988. Sequence in context: A295658 A307427 A318672 * A055229 A270419 A275216 Adjacent sequences:  A325986 A325987 A325988 * A325990 A325991 A325992 KEYWORD nonn AUTHOR Gus Wiseman, May 30 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.

Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)