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%I #10 Feb 15 2020 10:52:27
%S 6,21,26,51,1157,372101,1288005205276048901
%N Semiprimes pq such that pq - 1 divides p^2 + q^2 + 2.
%C Semiprimes pq such that pq-1 divides (p+q)^2.
%C The third to fifth terms are Fib(3)*Fib(7), Fib(7)*Fib(11) and Fib(13)*Fib(17).
%C Products of two prime Fibonacci numbers F(k) and F(k+4) (see A001605 and A005478) are in the sequence.
%C 6 and 26 are the only even terms. Odd terms contain products of pairs of consecutive terms from the following sequences: A005248, A001541, A033889, A033891. - _Max Alekseyev_, Aug 27 2009
%e The semiprime 6 = 2*3 is in the sequence because 2*3 - 1 = 5 divides 2^2 + 3^2 + 2 = 15.
%p isA001358 := proc(n) RETURN ( numtheory[bigomega](n) =2 ) ; end:
%p isA164698 := proc(n) if isA001358(n) then p := op(1,op(1,ifactors(n)[2]) ) ; q := n/p ; if (p^2+q^2+2) mod (p*q-1) = 0 then true; else false; fi; else false; fi; end:
%p for n from 4 to 3000000 do if isA164698(n) then print(n, ifactors(n)) ; fi; od: # _R. J. Mathar_, Aug 24 2009
%Y Cf. A001358, A000045, A140362, A164643.
%K nonn,more
%O 1,1
%A _Mohamed Bouhamida_, Aug 22 2009
%E Missing values added by _R. J. Mathar_, Aug 24 2009
%E a(7) from _Max Alekseyev_, Aug 27 2009
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