cp's OEIS Frontend

A325988 Number of covering (or complete) factorizations of n.

%I A325988 #5 May 31 2019 05:34:25
%S A325988 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 A325988 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 A325988 1,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1
%N A325988 Number of covering (or complete) factorizations of n.
%C A325988 First differs from A072911 at a(64) = 5, A072911(64) = 4.
%C A325988 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 A325988 a(2^n) = A126796(n).
%e A325988 The a(64) = 5 factorizations:
%e A325988   (2*2*2*2*2*2)
%e A325988   (2*2*2*2*4)
%e A325988   (2*2*2*8)
%e A325988   (2*2*4*4)
%e A325988   (2*4*8)
%e A325988 The a(96) = 4 factorizations:
%e A325988   (2*2*2*2*2*3)
%e A325988   (2*2*2*3*4)
%e A325988   (2*2*3*8)
%e A325988   (2*3*4*4)
%t A325988 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A325988 Table[Length[Select[facs[n],Union[Times@@@Subsets[#]]==Divisors[n]&]],{n,100}]
%Y A325988 Cf. A002033, A103295, A126796, A188431.
%Y A325988 Cf. A325684, A325781, A325786, A325788, A325986, A325989, A325990.
%K A325988 nonn
%O A325988 1,8
%A A325988 _Gus Wiseman_, May 30 2019