A330973 Least positive integer with exactly n factorizations into factors > 1, and 0 if no such number exists.

1, 4, 8, 12, 16, 0, 24, 0, 36, 0, 60, 48, 0, 0, 128, 72, 0, 0, 96, 0, 120, 256, 0, 0, 0, 180, 0, 0, 144, 192, 216, 0, 0, 0, 0, 420, 0, 240, 0, 0, 0, 1024, 0, 0, 384, 0, 288, 0, 0, 0, 0, 360, 0, 0, 0, 2048, 432, 0, 0, 0, 0, 0, 0, 480, 0, 900, 768, 0, 0, 0, 0, 0

Offset

1,2

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

R. E. Canfield, P. Erdős and C. Pomerance, On a Problem of Oppenheim concerning "Factorisatio Numerorum", J. Number Theory 17 (1983), 1-28.

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[fam[#]&, 2^nn];
Table[If[#=={}, 0, #[[1, 1]]]&[Position[nds, i]], {i, nn}]

Crossrefs

All nonzero terms belong to A025487.

Includes all highly factorable numbers A033833.

Factorizations are A001055, with image A045782.

The version without zeros is A045783.

The sorted version is A330972.

The strict version is A330974.

Positions of zeros are A330976.

Cf. A001055, A001222, A002033, A007716, A045778, A045779, A330935, A330992, A330997, A330998, A346426.

Sequence in context: A311115 A311116 A311117 * A242399 A081747 A331061

Adjacent sequences: A330970 A330971 A330972 * A330974 A330975 A330976

Keyword

nonn

Author

Gus Wiseman, Jan 06 2020

Extensions

More terms from Jinyuan Wang, Jul 07 2021

Status

approved