%I #7 Jan 13 2020 09:37:25

%S 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,

%T 41,42,43,44,45,47,48,49,50,52,53,54,56,59,60,61,63,66,67,68,70,71,72,

%U 73,75,76,78,79,80,83,84,88,89,90,92,97,98,99,100,101,102

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

%C First differs from A319237 in lacking 300.

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

%t Select[Range[100],OddQ[Length[strfacs[#]]]&]

%Y The version for strict integer partitions is A001318.

%Y The version for integer partitions is A052002.

%Y The version for set partitions appears to be A032766.

%Y The non-strict version is A331050.

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

%Y The even version is A331231.

%Y Factorizations are A001055 with image A045782 and complement A330976.

%Y Strict factorizations are A045778 with image A045779 and complement A330975.

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

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 12 2020