OFFSET
1,11
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1000
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.
EXAMPLE
a(11) = 2 with polynomials x^3 + 6*x^2 + 11*x + 6 = (x+1) * (x+2) * (x+3) and x^3 + 7*x^2 + 11*x + 5 = (x+1)^2 * (x+5). - Michael Somos, Feb 23 2014
MATHEMATICA
Table[p = Flatten[Table[{a, b, c, 1}, {a, n}, {b, n}, {c, n}], 2]; cnt = 0; Do[If[Max[p[[i]]] == n, poly = p[[i]].x^Range[0, 3]; r = Rest[FactorList[poly]]; If[Total[Transpose[r][[2]]] == 3 && Union[Coefficient[Transpose[r][[1]], x]] == {1}, Print[{n, r}]; cnt++]], {i, Length[p]}]; cnt, {n, 20}] (* T. D. Noe, Feb 22 2014 *)
PROG
(PARI) {a(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))))}; /* Michael Somos, Feb 23 2014 */
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 22 2014
EXTENSIONS
Definition corrected by Giovanni Resta, Feb 22 2014
Extended by T. D. Noe, Feb 22 2014
STATUS
approved