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A320891 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into squarefree semiprimes. 28
4, 9, 16, 24, 25, 40, 49, 54, 56, 64, 81, 88, 96, 104, 121, 135, 136, 144, 152, 160, 169, 184, 189, 224, 232, 240, 248, 250, 256, 289, 296, 297, 324, 328, 336, 344, 351, 352, 361, 375, 376, 384, 400, 416, 424, 459, 472, 486, 488, 513, 528, 529, 536, 544, 560 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A squarefree semiprime (A006881) is a product of any two distinct primes.
Also numbers with an even number x of prime factors, whose greatest prime multiplicity exceeds x/2.
LINKS
EXAMPLE
A complete list of all factorizations of 24 is:
(2*2*2*3),
(2*2*6), (2*3*4),
(2*12), (3*8), (4*6),
(24).
All of these contain at least one number that is not a squarefree semiprime, so 24 belongs to the sequence.
MATHEMATICA
semfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[semfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]];
Select[Range[100], And[EvenQ[PrimeOmega[#]], semfacs[#]=={}]&]
CROSSREFS
Sequence in context: A320894 A122986 A066427 * A161697 A078593 A168350
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)