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%I #18 May 11 2019 18:32:21
%S 5,10,15,20,21,25,30,32,35,40,43,45,49,50,54,55,60,65,66,70,75,76,80,
%T 83,85,87,89,90,95,98,100,105,109,110,112,115,117,120,125,130,131,134,
%U 135,140,141,142,145,150,151,153,155,158,160,164,165,168,170,175
%N Numbers k such that 6k-5 is a composite number of the form (6x-1) * (6y-1).
%C Numbers whose associate in A091300 has at least one factorization into two factors of A016969.
%e n=5 is in the sequence because 6*5-5 = 25 = 5*5 with x = y = 1.
%e n=10 is in the sequence because 6*10-5 = 55 = 5*11 with x=1, y=2.
%p isA016969 := proc(n)
%p (n mod 6)=5 ;
%p end proc:
%p isA016921 := proc(n)
%p (n mod 6)=1 ;
%p end proc:
%p isA091300 := proc(n)
%p (not isprime(n)) and isA016921(n) ;
%p end proc:
%p isA199860 := proc(n)
%p if isA091300(6*n-5) then
%p for d in numtheory[divisors](6*n-5) minus {1} do
%p if isA016969(d) and isA016969((6*n-5)/d) then
%p return true;
%p end if;
%p end do:
%p return false;
%p else
%p return false;
%p end if;
%p end proc:
%p for n from 5 to 210 do
%p if isA199860(n) then
%p printf("%d,",n) ;
%p end if ;
%p end do; # _R. J. Mathar_, Nov 27 2011
%Y Cf. A199859.
%K nonn,easy
%O 1,1
%A _Eleonora Echeverri-Toro_, Nov 11 2011
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