cp's OEIS Frontend

A320911 Numbers with an even number of prime factors (counted with multiplicity) that can be factored into squarefree semiprimes.

%I A320911 #13 Feb 02 2021 04:35:19
%S A320911 1,6,10,14,15,21,22,26,33,34,35,36,38,39,46,51,55,57,58,60,62,65,69,
%T A320911 74,77,82,84,85,86,87,90,91,93,94,95,100,106,111,115,118,119,122,123,
%U A320911 126,129,132,133,134,140,141,142,143,145,146,150,155,156,158,159
%N A320911 Numbers with an even number of prime factors (counted with multiplicity) that can be factored into squarefree semiprimes.
%C A320911 A squarefree semiprime (A006881) is a product of any two distinct primes.
%C A320911 Also numbers with an even number x of prime factors, whose prime multiplicities do not exceed x/2.
%H A320911 Amiram Eldar, <a href="/A320911/b320911.txt">Table of n, a(n) for n = 1..10000</a>
%e A320911 360 is in the sequence because it can be factored into squarefree semiprimes as (6*6*10).
%e A320911 4620 is in the sequence, and can be factored into squarefree semiprimes in 6 ways: (6*10*77), (6*14*55), (6*22*35), (10*14*33), (10*21*22), (14*15*22).
%t A320911 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]&]}]];
%t A320911 Select[Range[100],And[EvenQ[PrimeOmega[#]],sqfsemfacs[#]!={}]&]
%Y A320911 Cf. A001055, A001222, A001358, A005117, A006881, A007717, A028260, A320655, A320656, A320891, A320892, A320893, A320894, A320912.
%K A320911 nonn
%O A320911 1,2
%A A320911 _Gus Wiseman_, Oct 23 2018