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

1,1

Comments

Warning: I have only confirmed the first eight terms. The rest are derived from A045782. - Gus Wiseman, Jan 07 2020

Links

Table of n, a(n) for n=1..65.

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=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]

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.

Sequence in context: A343569 A331549 A184111 * A181764 A153032 A086822

Adjacent sequences: A330973 A330974 A330975 * A330977 A330978 A330979

Keyword

nonn

Author

Gus Wiseman, Jan 07 2020

Status

approved