A330976 Numbers that are not the number of factorizations into factors > 1 of any positive integer.

6, 8, 10, 13, 14, 17, 18, 20, 23, 24, 25, 27, 28, 32, 33, 34, 35, 37, 39, 40, 41, 43, 44, 46, 48, 49, 50, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 65, 68, 69, 70, 71, 72, 73, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 99

Offset: 1

Author

Gus Wiseman, Jan 07 2020

Keywords

• nonn

Comments

Warning: I have only confirmed the first eight terms. The rest are derived from A045782. - 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 A045782.

The strict version is A330975.

Factorizations are A001055, with image A045782.

Strict factorizations are A045778, with image A045779.

The least number with n factorizations is A330973(n).

Cf. A033833, A045779, A045783, A317145, A330935, A330972, A330974, A330977, A330991.

Programs

Mathematica

nn=15;
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];
Complement[Range[nn],nds]