A330975 Numbers that are not the number of factorizations of n into distinct factors > 1 for any n.

11, 13, 20, 23, 24, 26, 28, 29, 30, 35, 36, 37, 39, 41, 45, 47, 48, 49, 50, 51, 53, 58, 60, 62, 63, 65, 66, 68, 69, 71, 72, 73, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87, 90, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 106, 107, 108, 109, 113, 114, 115, 118

Offset: 1

Author

Gus Wiseman, Jan 07 2020

Keywords

• nonn

Comments

Warning: I have only confirmed the first three terms. The rest are derived from A045779. - Gus Wiseman, Jan 07 2020

Links

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

Crossrefs

Complement of A045779.

The non-strict version is A330976.

Factorizations are A001055, with image A045782, with complement A330976.

Strict factorizations are A045778, with image A045779.

The least positive integer with n strict factorizations is A330974(n).

Cf. A001222, A002033, A025487, A033833, A045780, A045783, A318286, A328966, A330972, A330973, A330997.

Programs

Mathematica

nn=20;
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];
Complement[Range[nn],nds]