A124579 Number of natural numbers less than n which have identical Moebius mu values.
0, 0, 1, 0, 2, 1, 3, 1, 2, 2, 4, 3, 5, 3, 4, 4, 6, 5, 7, 6, 5, 6, 8, 7, 8, 7, 9, 10, 9, 10, 11, 11, 8, 9, 10, 12, 12, 11, 12, 13, 13, 14, 15, 14, 15, 13, 16, 16, 17, 18, 14, 19, 17, 20, 15, 21, 16, 17, 18, 22, 19, 18, 23, 24, 19, 20, 21, 25, 20, 22, 23, 26, 24, 21, 27, 28, 22, 25, 26, 29
Offset: 1
Keywords
Examples
a(10) = 2 because in the first nine integers less than 10, mu(1) = mu(6) = mu(10).
Programs
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Mathematica
a[n_] := a[n] = MoebiusMu@n; f[n_] := Count[a /@ Range[n - 1], a@n]; Array[f, 80] With[{mu=MoebiusMu[Range[80]]},Table[Count[Take[mu,n],?(#==MoebiusMu[ n+1]&)],{n,0,Length[mu]}]] (* _Harvey P. Dale, Aug 18 2016 *)