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A325988 Number of covering (or complete) factorizations of n. 7
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

First differs from A072911 at a(64) = 5, A072911(64) = 4.

A covering factorization of n is an orderless factorization of n into factors > 1 such that every divisor of n is the product of some submultiset of the factors.

LINKS

Table of n, a(n) for n=1..87.

FORMULA

a(2^n) = A126796(n).

EXAMPLE

The a(64) = 5 factorizations:

  (2*2*2*2*2*2)

  (2*2*2*2*4)

  (2*2*2*8)

  (2*2*4*4)

  (2*4*8)

The a(96) = 4 factorizations:

  (2*2*2*2*2*3)

  (2*2*2*3*4)

  (2*2*3*8)

  (2*3*4*4)

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], Union[Times@@@Subsets[#]]==Divisors[n]&]], {n, 100}]

CROSSREFS

Cf. A002033, A103295, A126796, A188431.

Cf. A325684, A325781, A325786, A325788, A325986, A325989, A325990.

Sequence in context: A325837 A050361 A072911 * A328856 A053150 A295657

Adjacent sequences:  A325985 A325986 A325987 * A325989 A325990 A325991

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 30 2019

STATUS

approved

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Last modified March 29 18:35 EDT 2020. Contains 333117 sequences. (Running on oeis4.)