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 A164698 Semiprimes pq such that pq - 1 divides p^2 + q^2 + 2. 0
 6, 21, 26, 51, 1157, 372101, 1288005205276048901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Semiprimes pq such that pq-1 divides (p+q)^2. The third to fifth terms are Fib(3)*Fib(7), Fib(7)*Fib(11) and Fib(13)*Fib(17). Products of two prime Fibonacci numbers F(k) and F(k+4) (see A001605 and A005478) are in the sequence. 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 LINKS EXAMPLE The semiprime 6 = 2*3 is in the sequence because 2*3 - 1 = 5 divides 2^2 + 3^2 + 2 = 15. MAPLE isA001358 := proc(n) RETURN ( numtheory[bigomega](n) =2 ) ; end: isA164698 := proc(n) if isA001358(n) then p := op(1, op(1, ifactors(n)) ) ; q := n/p ; if (p^2+q^2+2) mod (p*q-1) = 0 then true; else false; fi; else false; fi; end: for n from 4 to 3000000 do if isA164698(n) then print(n, ifactors(n)) ; fi; od: # R. J. Mathar, Aug 24 2009 CROSSREFS Cf. A001358, A000045, A140362, A164643. Sequence in context: A323917 A327865 A229498 * A020880 A046467 A132184 Adjacent sequences:  A164695 A164696 A164697 * A164699 A164700 A164701 KEYWORD nonn,more AUTHOR Mohamed Bouhamida, Aug 22 2009 EXTENSIONS Missing values added by R. J. Mathar, Aug 24 2009 a(7) from Max Alekseyev, Aug 27 2009 STATUS approved

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Last modified May 12 13:02 EDT 2021. Contains 343823 sequences. (Running on oeis4.)