cp's OEIS Frontend

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

%I A331230 #7 Jan 13 2020 09:37:25
%S A331230 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 A331230 41,42,43,44,45,47,48,49,50,52,53,54,56,59,60,61,63,66,67,68,70,71,72,
%U A331230 73,75,76,78,79,80,83,84,88,89,90,92,97,98,99,100,101,102
%N A331230 Numbers k such that the number of factorizations of k into distinct factors > 1 is odd.
%C A331230 First differs from A319237 in lacking 300.
%t A331230 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A331230 Select[Range[100],OddQ[Length[strfacs[#]]]&]
%Y A331230 The version for strict integer partitions is A001318.
%Y A331230 The version for integer partitions is A052002.
%Y A331230 The version for set partitions appears to be A032766.
%Y A331230 The non-strict version is A331050.
%Y A331230 The version for primes (instead of odds) is A331201.
%Y A331230 The even version is A331231.
%Y A331230 Factorizations are A001055 with image A045782 and complement A330976.
%Y A331230 Strict factorizations are A045778 with image A045779 and complement A330975.
%Y A331230 The least number with n strict factorizations is A330974(n).
%Y A331230 Cf. A035359, A045780, A318286, A328966, A330991, A330997, A331051, A331200, A331232.
%K A331230 nonn
%O A331230 1,2
%A A331230 _Gus Wiseman_, Jan 12 2020