A331231 Numbers 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

Offset: 1

Author

Gus Wiseman, Jan 12 2020

Keywords

• nonn

Comments

First differs from A319238 in having 300.

Crossrefs

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.

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],EvenQ[Length[strfacs[#]]]&]