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%I #13 Sep 04 2023 15:48:36
%S 5,20,32,41,124,133,140,160,189,224,257,265,284,292,305,320,445,509,
%T 581,644,673,945,985,1076,1085,1120,1280,1345,1436,1489,1541,1597,
%U 1708,1772,1917,2048,2237,2273,2336,2345,2489,2624,2749,2889,2980,3105,3140,3205
%N Positive numbers of the form p^6 - 4*p^4*q + 4*p^2*q^2 + 4*q^3 (and p*q <> 0).
%C Conjecture: There are no perfect squares in this sequence (in spite of all numbers being congruent to 0 or 1 mod 4).
%C If any perfect square occurred in this sequence then a septic trinomial x^7 + A*x^2 + B with two irreducible factors of degree 3 and 4 would exist.
%C This sequence is a subsequence of A079896.
%t aa = {}; Do[Do[kk = p^6 - 4 p^4 q + 4 p^2 q^2 + 4 q^3; If[(kk > 0) && (p q != 0), AppendTo[aa, kk]], {p, 1, 200}], {q, -200, 200}]; Take[Union[aa], 100]
%Y Cf. A079896.
%K nonn
%O 1,1
%A _Artur Jasinski_, May 30 2010