A238098 Number of cubic polynomials with coefficients from {1..n} for which all three roots are integers.

0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 13, 15, 19, 21, 23, 25, 27, 30, 34, 36, 39, 44, 46, 49, 54, 57, 60, 64, 67, 72, 76, 79, 85, 91, 92, 95, 100, 106, 109, 115, 117, 122, 129, 132, 136, 147, 150, 154, 159, 163, 166, 174, 180, 187, 191, 194, 199, 210, 211, 216

Offset

1,5

Comments

A generalization of A006218 and A238096.

Links

Table of n, a(n) for n=1..62.

Dorin Andrica and Eugen J. Ionascu, On the number of polynomials with coefficients in [n], An. St. Univ. Ovidius Constanta, Vol. 22(1),2014, 13-23.

Formula

a(n) = Sum_{k=1..n} floor(n/k)*A238097(k).

Prog

(PARI) f(n) = if( n<1, 0, sum(a1=1, n, sum(a2=1, n, sum(a3=1, n, vecmax([a1, a2, a3]) == n && vecsum( factor( Pol([1, a1, a2, a3]))[, 2]) == 3)))); \\ A238097
a(n) = sum(k=1, n, (n\k)*f(k));
lista(nn) = my(v = vector(nn, k, f(k))); vector(nn, i, sum(k=1, i, (i\k)*v[k])); \\ Michel Marcus, Sep 28 2023

Crossrefs

Cf. A006218, A238096, A238097.

Sequence in context: A184105 A062469 A340758 * A328283 A034156 A034157

Adjacent sequences: A238095 A238096 A238097 * A238099 A238100 A238101

Keyword

nonn

Author

N. J. A. Sloane, Feb 22 2014

Status

approved