%I #8 Jul 07 2021 09:26:34

%S 1,6,12,64,24,256,48,512,60,96,0,2048,0,144,210,120,216,180,384,0,288,

%T 16384,0,0,240,0,432,0,0,0,420,65536,1536,360,0,0,0,480,0,900,0,864,

%U 3072,1152,0,1296,0,0,0,0,0,2310,0,524288,6144,960,720,0,840,0,2304

%N Least positive integer with n factorizations into distinct factors > 1, and 0 if no such number exists.

%t nn=10;

%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 Table[If[#=={},0,#[[1,1]]]&[Position[nds,i]],{i,nn}]

%Y All nonzero terms belong to A025487.

%Y Strict factorizations are A045778, with image A045779.

%Y The version with zeros removed is A045780.

%Y The non-strict version is A330973.

%Y Positions of zeros are A330975.

%Y The sorted version is A330997.

%Y Cf. A001055, A001222, A033833, A045782, A045783, A318286, A328966, A330972.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 06 2020

%E More terms from _Jinyuan Wang_, Jul 07 2021