A331050 Positive integers whose number of factorizations into factors > 1 (A001055) is odd.

1, 2, 3, 5, 7, 8, 11, 13, 16, 17, 19, 23, 24, 27, 29, 30, 31, 32, 36, 37, 40, 41, 42, 43, 47, 53, 54, 56, 59, 60, 61, 64, 66, 67, 70, 71, 73, 78, 79, 81, 83, 84, 88, 89, 90, 96, 97, 100, 101, 102, 103, 104, 105, 107, 109, 110, 113, 114, 120, 125, 126, 127, 128

Offset: 1

Author

Gus Wiseman, Jan 10 2020

Keywords

• nonn

Comments

First differs from A319239 in lacking 256.

Crossrefs

Complement of A331051.

The version for powers of two (instead of odds) is A330977.

The version for primes (instead of odds) is A330991.

Cf. A001055, A001221, A001222, A002033, A005117, A045778, A045782, A045783, A330972, A330973.

Programs

Mathematica

facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
Select[Range[100],OddQ[Length[facs[#]]]&]