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).

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

Links

Table of n, a(n) for n=1..54.

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[#]=={}]&]

Crossrefs

Cf. A001055, A001222, A001358, A005117, A006881, A007717, A025487, A028260, A320655, A320656, A320891, A320892, A320893, A320894, A320911, A320912.

Sequence in context: A062775 A288105 A288101 * A329879 A320059 A270450

Adjacent sequences: A320910 A320911 A320912 * A320914 A320915 A320916

Keyword

nonn

Author

Gus Wiseman, Oct 23 2018

Status

approved