A331230 Numbers k such that the number of factorizations of k into distinct factors > 1 is odd.

1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 17, 18, 19, 20, 23, 24, 25, 28, 29, 30, 31, 32, 36, 37, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 59, 60, 61, 63, 66, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 83, 84, 88, 89, 90, 92, 97, 98, 99, 100, 101, 102

Offset: 1

Author

Gus Wiseman, Jan 12 2020

Keywords

• nonn

Comments

First differs from A319237 in lacking 300.

Crossrefs

The version for strict integer partitions is A001318.

The version for integer partitions is A052002.

The version for set partitions appears to be A032766.

The non-strict version is A331050.

The version for primes (instead of odds) is A331201.

The even version is A331231.

Factorizations are A001055 with image A045782 and complement A330976.

Strict factorizations are A045778 with image A045779 and complement A330975.

The least number with n strict factorizations is A330974(n).

Cf. A035359, A045780, A318286, A328966, A330991, A330997, A331051, A331200, A331232.

Programs

Mathematica

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