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A238098 Number of cubic polynomials with coefficients from {1..n} for which all three roots are integers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
A generalization of A006218 and A238096.
LINKS
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
Sequence in context: A184105 A062469 A340758 * A328283 A034156 A034157
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 22 2014
STATUS
approved

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Last modified April 24 05:36 EDT 2024. Contains 371918 sequences. (Running on oeis4.)