%I #20 Sep 28 2023 12:34:17

%S 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,

%T 54,57,60,64,67,72,76,79,85,91,92,95,100,106,109,115,117,122,129,132,

%U 136,147,150,154,159,163,166,174,180,187,191,194,199,210,211,216

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

%C A generalization of A006218 and A238096.

%H 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.

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

%o (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

%o a(n) = sum(k=1, n, (n\k)*f(k));

%o 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

%Y Cf. A006218, A238096, A238097.

%K nonn

%O 1,5

%A _N. J. A. Sloane_, Feb 22 2014