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%I #13 Apr 20 2024 16:36:16
%S 44,12,44,32,64,1344,576,1344,832,275,4170,2375,3750,4060,128700,
%T 13243,1510620,24000,3348800,8788,467961,51072,133440,474214,61500,
%U 128700,85683,514098,509197,199927,24000,3720000,21376538,210990,486343,114244,12681084
%N Consider primitive pairs of integers (b, c) with b > 0 such that x^5 + b*x + c = 0 is irreducible and solvable by radicals: sequence gives values of c.
%C See A371553.
%H Ben Whitmore, <a href="/A371554/b371554.txt">Table of n, a(n) for n = 1..95</a>
%F x^5 + A371553(n)*x + a(n) is irreducible and solvable by radicals.
%e a(1) = 44 because A371553(1) = 11, and x^5 + 11*x + 44 is irreducible and solvable by radicals, and (11, 44) is a primitive pair.
%t pairs = Join @@ Table[
%t Select[{m, Abs[#1 - b] #2/5} & @@@
%t Sort[SolveValues[x^2 - (6b + 5y^4)x + 25b^2 == 0 && y > 0, {x, y},
%t Integers]],
%t Max[Last /@ FactorInteger[GCD @@ #]] < 4 &&
%t AllTrue[#, IntegerQ] &&
%t IrreduciblePolynomialQ[x^5 + #1x + #2 & @@ #] &
%t ],
%t {b, 1, 1000}
%t ];
%t pairs[[All, 2]]
%Y For values of b see A371553.
%K nonn
%O 1,1
%A _Ben Whitmore_, Mar 27 2024
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