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A358400 a(n) is the number of reducible monic quintic polynomials (x^5 + r*x^4 + s*x^3 + t*x^2 + u*x + v) with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t), abs(u), abs(v) <= n).

%I A358400 #26 Jan 02 2023 09:01:48
%S A358400 139,1313,5359,15365,34229,68385,120421,200839,312057,468827,669591,
%T A358400 943175,1274089,1701441,2216841,2856379,3594651,4510437,5541135,
%U A358400 6788823,8195941,9845089,11670925,13842429,16191555
%N A358400 a(n) is the number of reducible monic quintic polynomials (x^5 + r*x^4 + s*x^3 + t*x^2 + u*x + v) with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t), abs(u), abs(v) <= n).
%o A358400 (PARI)
%o A358400 { a(n) = \\ A358400
%o A358400     my( ct = 0 );
%o A358400     for (c1 = -n, n,
%o A358400     for (c2 = -n, n,
%o A358400     for (c3 = -n, n,
%o A358400     for (c4 = -n, n,
%o A358400     for (c5 = -n, n,
%o A358400         if ( ! polisirreducible( Pol([1,c1,c2,c3,c4,c5]) ), ct += 1 );
%o A358400     ); ); ); ); );
%o A358400     return( ct );
%o A358400 }
%o A358400 vector(7, n, a(n) )
%o A358400 \\ _Joerg Arndt_, Dec 05 2022
%Y A358400 Cf. A358398, A358399, A067274.
%K A358400 nonn,more
%O A358400 1,1
%A A358400 _Lorenz H. Menke, Jr._, Nov 13 2022