The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A238098

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A238098

Number of cubic polynomials with coefficients from {1..n} for which all three roots are integers.
(history; published version)

#20 by Michael De Vlieger at Thu Sep 28 12:34:17 EDT 2023

STATUS

proposed

approved

#19 by Michel Marcus at Thu Sep 28 12:15:00 EDT 2023

STATUS

editing

proposed

#18 by Michel Marcus at Thu Sep 28 12:14:40 EDT 2023

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.

STATUS

approved

editing

#17 by Michael De Vlieger at Thu Sep 28 12:07:26 EDT 2023

STATUS

reviewed

approved

#16 by Alois P. Heinz at Thu Sep 28 12:02:56 EDT 2023

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proposed

reviewed

#15 by Alois P. Heinz at Thu Sep 28 12:02:51 EDT 2023

STATUS

editing

proposed

#14 by Alois P. Heinz at Thu Sep 28 12:02:48 EDT 2023

DATA

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

STATUS

reviewed

editing

#13 by Joerg Arndt at Thu Sep 28 11:29:33 EDT 2023

STATUS

proposed

reviewed

#12 by Michel Marcus at Thu Sep 28 10:25:39 EDT 2023

STATUS

editing

proposed

#11 by Michel Marcus at Thu Sep 28 09:56:39 EDT 2023

REFERENCES

D. Andrica and E. J. Ionascu, On the number of polynomials with coefficients in [n], An. St. Univ. Ovidius Constanta, 2013, to appear.

LINKS

Dorin Andrica and Eugen J. Ionascu, <a href="http://www.emis.de/journals/ASUO/mathematics_/vol22-1/Andrica_D__Ionascu_E.J._nou-1__final_.pdf">On the number of polynomials with coefficients in [n]</a>, An. St. Univ. Ovidius Constanta, Vol. 22(1),2014, 13-23.

STATUS

approved

editing