A077599 Sequence of n such that -1 is a "double" root for M(n,x) (i.e., M(n,x)=(x+1)^2*Q(n,x)).

8, 9, 24, 45, 100, 117, 120, 125, 135, 171, 175, 180, 184, 224, 243, 248, 256, 261, 270, 304, 312, 324, 342, 343, 344, 360, 369, 405, 459, 468, 472, 475, 477, 486, 507, 513, 520, 531, 536, 578, 584, 603, 608, 625, 639, 640, 657, 664, 675, 704, 711, 720, 728

Offset: 1

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Keywords

• nonn

Comments

The n-th Moebius polynomial M(n,x) satisfies M(n,-1)=mu(n), the Moebius function of n; thus -1 is a simple root of M(n,x) if n is not squarefree. Hence these values could be called "double nonsquarefree numbers".

The n-th polynomial is divisible by (x+1)^3 for n=175, 343, 513, 800, 875. - T. D. Noe, Jan 09 2008

Crossrefs

Cf. A074586, A074587, A077596, A077597, A077598, A077600, A077601.

Programs

Mathematica

a[n_,1]=1; a[n_,k_]:=a[n, k]=Sum[Floor[n/m] a[m,k-1], {m,n-1}]; t={}; Do[p=Table[a[n,k], {k,n}].(x^Range[0,n-1]); If[PolynomialMod[p,(x+1)^2]==0, AppendTo[t,n]], {n,100}]; t (* T. D. Noe, Jan 09 2008 *)

Extensions

More terms from T. D. Noe, Jan 09 2008