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).

139, 1313, 5359, 15365, 34229, 68385, 120421, 200839, 312057, 468827, 669591, 943175, 1274089, 1701441, 2216841, 2856379, 3594651, 4510437, 5541135, 6788823, 8195941, 9845089, 11670925, 13842429, 16191555

Offset: 1

Author

Lorenz H. Menke, Jr., Nov 13 2022

Keywords

• nonn
• more

Crossrefs

Cf. A358398, A358399, A067274.

Programs

PARI

{ a(n) = \\ A358400
    my( ct = 0 );
    for (c1 = -n, n,
    for (c2 = -n, n,
    for (c3 = -n, n,
    for (c4 = -n, n,
    for (c5 = -n, n,
        if ( ! polisirreducible( Pol([1,c1,c2,c3,c4,c5]) ), ct += 1 );
    ); ); ); ); );
    return( ct );
}
vector(7, n, a(n) )
\\ Joerg Arndt, Dec 05 2022