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