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A320913
Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into squarefree semiprimes (A320891) but can be factored into distinct semiprimes (A320912).
1
4, 9, 24, 25, 40, 49, 54, 56, 88, 104, 121, 135, 136, 152, 169, 184, 189, 232, 240, 248, 250, 289, 296, 297, 328, 336, 344, 351, 361, 375, 376, 424, 459, 472, 488, 513, 528, 529, 536, 560, 568, 584, 621, 624, 632, 664, 686, 712, 776, 783, 808, 810, 816, 824
OFFSET
1,1
COMMENTS
A semiprime (A001358) is a product of any two not necessarily distinct primes.
If A025487(k) is contained in this sequence then so is every positive integer with its prime signature. - David A. Corneth, Oct 24 2018
MATHEMATICA
sqfsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sqfsemfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]];
strsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strsemfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], PrimeOmega[#]==2&]}]];
Select[Range[1000], And[EvenQ[PrimeOmega[#]], strsemfacs[#]!={}, sqfsemfacs[#]=={}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved