proposed

approved

editing

proposed

allocated for Gus WisemanNumbers k such that the number of factorizations of k into distinct factors > 1 is even.

6, 8, 10, 14, 15, 16, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 64, 65, 69, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 96, 106, 111, 115, 118, 119, 120, 122, 123, 125, 129, 133, 134, 141, 142, 143, 144, 145, 146, 155, 158, 159, 160, 161, 166

1,1

First differs from A319238 in having 300.

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

Select[Range[100], EvenQ[Length[strfacs[#]]]&]

The version for integer partitions is A001560.

The version for strict integer partitions is A090864.

The version for set partitions appears to be A016789.

The non-strict version is A331051.

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

The odd version is A331230.

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. A001318, A045780, A045783, A318286, A328966, A330973, A330991, A330997, A331022, A331023/A331024, A331050, A331200, A331232.

allocated

nonn

Gus Wiseman, Jan 12 2020

approved

editing

allocated for Gus Wiseman

allocated

approved