A330974 Least positive integer with n factorizations into distinct factors > 1, and 0 if no such number exists.

1, 6, 12, 64, 24, 256, 48, 512, 60, 96, 0, 2048, 0, 144, 210, 120, 216, 180, 384, 0, 288, 16384, 0, 0, 240, 0, 432, 0, 0, 0, 420, 65536, 1536, 360, 0, 0, 0, 480, 0, 900, 0, 864, 3072, 1152, 0, 1296, 0, 0, 0, 0, 0, 2310, 0, 524288, 6144, 960, 720, 0, 840, 0, 2304

Offset: 1

Author

Gus Wiseman, Jan 06 2020

Keywords

• nonn

Crossrefs

All nonzero terms belong to A025487.

Strict factorizations are A045778, with image A045779.

The version with zeros removed is A045780.

The non-strict version is A330973.

Positions of zeros are A330975.

The sorted version is A330997.

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

Programs

Mathematica

nn=10;
fam[n_]:=fam[n]=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[fam[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
nds=Length/@Array[Select[fam[#],UnsameQ@@#&]&,2^nn];
Table[If[#=={},0,#[[1,1]]]&[Position[nds,i]],{i,nn}]

Extensions

More terms from Jinyuan Wang, Jul 07 2021