|
|
A331231
|
|
Numbers k such that the number of factorizations of k into distinct factors > 1 is even.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
First differs from A319238 in having 300.
|
|
LINKS
|
|
|
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[#]]]&]
|
|
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 version for primes (instead of evens) is A331201.
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|