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

1,2

Links

Table of n, a(n) for n=1..61.

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}]

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.

Sequence in context: A299855 A121735 A070970 * A045780 A088726 A163342

Adjacent sequences: A330971 A330972 A330973 * A330975 A330976 A330977

Keyword

nonn

Author

Gus Wiseman, Jan 06 2020

Extensions

More terms from Jinyuan Wang, Jul 07 2021

Status

approved