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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 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.)