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%I #11 Jan 26 2020 20:42:45
%S 11,13,20,23,24,26,28,29,30,35,36,37,39,41,45,47,48,49,50,51,53,58,60,
%T 62,63,65,66,68,69,71,72,73,75,77,78,79,81,82,84,85,86,87,90,92,94,95,
%U 96,97,98,99,101,102,103,105,106,107,108,109,113,114,115,118
%N Numbers that are not the number of factorizations of n into distinct factors > 1 for any n.
%C Warning: I have only confirmed the first three terms. The rest are derived from A045779. - _Gus Wiseman_, Jan 07 2020
%H R. E. Canfield, P. Erdős and C. Pomerance, <a href="http://math.dartmouth.edu/~carlp/PDF/paper39.pdf">On a Problem of Oppenheim concerning "Factorisatio Numerorum"</a>, J. Number Theory 17 (1983), 1-28.
%t nn=20;
%t fam[n_]:=fam[n]=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[fam[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t nds=Length/@Array[Select[fam[#],UnsameQ@@#&]&,2^nn];
%t Complement[Range[nn],nds]
%Y Complement of A045779.
%Y The non-strict version is A330976.
%Y Factorizations are A001055, with image A045782, with complement A330976.
%Y Strict factorizations are A045778, with image A045779.
%Y The least positive integer with n strict factorizations is A330974(n).
%Y Cf. A001222, A002033, A025487, A033833, A045780, A045783, A318286, A328966, A330972, A330973, A330997.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jan 07 2020
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