A077600 Number of real roots for the n-th Moebius polynomial, M(n,x), which satisfies M(n,-1)=mu(n) the Moebius function of n.

0, 1, 2, 3, 2, 3, 2, 5, 4, 3, 2, 5, 4, 3, 4, 5, 4, 5, 2, 5, 4, 3, 2, 7, 6, 5, 6, 5, 4, 5, 4, 7, 4, 5, 4, 7, 6, 5, 6, 7, 4, 5, 4, 5, 6, 5, 4, 7, 6, 7, 6, 5, 4, 7, 4, 5, 4, 5, 4, 7, 6, 5, 8, 7, 6, 5, 6, 9, 6, 5, 4, 9, 8, 5, 8, 9, 4, 5, 4, 7, 8, 7, 4, 7, 6, 7, 6, 7, 4, 9, 4, 7, 8, 5, 6, 7, 6, 9, 8

Offset

1,3

Links

Table of n, a(n) for n=1..99.

Mathematica

m[1, x_] = 1; m[n_, x_] :=  m[n, x] = 1 + Sum[x*m[k, x]*Floor[n/k], {k, 1, n-1}] // Expand; a[n_] := CountRoots[m[n, x], x]; Table[a[n], {n, 1, 99}] (* Jean-François Alcover, Sep 13 2012 *)

Crossrefs

Cf. A074586, A074587, A077596, A077597, A077598, A077599, A077601.

Sequence in context: A229708 A204895 A064652 * A120223 A282691 A346744

Adjacent sequences: A077597 A077598 A077599 * A077601 A077602 A077603

Keyword

nonn

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Extensions

Typo (?) a(45)=4 replaced with 6 by Jean-François Alcover, Sep 13 2012

Status

approved