A320894 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into distinct squarefree semiprimes.

4, 9, 16, 24, 25, 36, 40, 49, 54, 56, 64, 81, 88, 96, 100, 104, 121, 135, 136, 144, 152, 160, 169, 184, 189, 196, 216, 224, 225, 232, 240, 248, 250, 256, 289, 296, 297, 324, 328, 336, 344, 351, 352, 360, 361, 375, 376, 384, 400, 416, 424, 441, 459, 472, 484

Offset

1,1

Comments

A squarefree semiprime (A006881) is a product of any two distinct primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

A complete list of all strict factorizations of 24 is: (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

strsqfsemfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strsqfsemfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], And[SquareFreeQ[#], PrimeOmega[#]==2]&]}]];
Select[Range[100], And[EvenQ[PrimeOmega[#]], strsqfsemfacs[#]=={}]&]

Crossrefs

Cf. A001055, A001358, A005117, A006881, A007717, A028260, A318871, A318953, A320655, A320656, A320891, A320892, A320893.

Sequence in context: A168086 A176238 A139588 * A122986 A066427 A320891

Adjacent sequences: A320891 A320892 A320893 * A320895 A320896 A320897

Keyword

nonn

Author

Gus Wiseman, Oct 23 2018

Status

approved