A358400 - OEIS

%I #26 Jan 02 2023 09:01:48

%S 139,1313,5359,15365,34229,68385,120421,200839,312057,468827,669591,

%T 943175,1274089,1701441,2216841,2856379,3594651,4510437,5541135,

%U 6788823,8195941,9845089,11670925,13842429,16191555

%N 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 (PARI)

%o { a(n) = \\ A358400

%o     my( ct = 0 );

%o     for (c1 = -n, n,

%o     for (c2 = -n, n,

%o     for (c3 = -n, n,

%o     for (c4 = -n, n,

%o     for (c5 = -n, n,

%o         if ( ! polisirreducible( Pol([1,c1,c2,c3,c4,c5]) ), ct += 1 );

%o     ); ); ); ); );

%o     return( ct );

%o }

%o vector(7, n, a(n) )

%o \\ _Joerg Arndt_, Dec 05 2022

%Y Cf. A358398, A358399, A067274.

%K nonn,more

%O 1,1

%A _Lorenz H. Menke, Jr._, Nov 13 2022