A124579 - OEIS

%I #4 Aug 18 2016 14:14:36

%S 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,

%T 8,9,10,12,12,11,12,13,13,14,15,14,15,13,16,16,17,18,14,19,17,20,15,

%U 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

%N Number of natural numbers less than n which have identical Moebius mu values.

%e a(10) = 2 because in the first nine integers less than 10, mu(1) = mu(6) = mu(10).

%t a[n_] := a[n] = MoebiusMu@n; f[n_] := Count[a /@ Range[n - 1], a@n]; Array[f, 80]

%t With[{mu=MoebiusMu[Range[80]]},Table[Count[Take[mu,n],_?(#==MoebiusMu[ n+1]&)],{n,0,Length[mu]}]] (* _Harvey P. Dale_, Aug 18 2016 *)

%Y Cf. A124580.

%Y Cf. A008683, A002321.

%K nonn

%O 1,5

%A _Robert G. Wilson v_, Nov 05 2006