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%I #5 May 31 2019 05:34:25
%S 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,
%T 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,
%U 1,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1
%N Number of covering (or complete) factorizations of n.
%C First differs from A072911 at a(64) = 5, A072911(64) = 4.
%C 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.
%F a(2^n) = A126796(n).
%e The a(64) = 5 factorizations:
%e (2*2*2*2*2*2)
%e (2*2*2*2*4)
%e (2*2*2*8)
%e (2*2*4*4)
%e (2*4*8)
%e The a(96) = 4 factorizations:
%e (2*2*2*2*2*3)
%e (2*2*2*3*4)
%e (2*2*3*8)
%e (2*3*4*4)
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t Table[Length[Select[facs[n],Union[Times@@@Subsets[#]]==Divisors[n]&]],{n,100}]
%Y Cf. A002033, A103295, A126796, A188431.
%Y Cf. A325684, A325781, A325786, A325788, A325986, A325989, A325990.
%K nonn
%O 1,8
%A _Gus Wiseman_, May 30 2019