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

1,1

Comments

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

Links

Table of n, a(n) for n=1..62.

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=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]

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.

Sequence in context: A235479 A089774 A346287 * A351841 A257864 A248599

Adjacent sequences: A330972 A330973 A330974 * A330976 A330977 A330978

Keyword

nonn

Author

Gus Wiseman, Jan 07 2020

Status

approved