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A330975
Numbers that are not the number of factorizations of n into distinct factors > 1 for any n.
12
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
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).
Sequence in context: A235479 A089774 A346287 * A351841 A257864 A248599
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 07 2020
STATUS
approved