Moebius Mu function

[Ed Pegg Jr]

I recently wrote a column for maa.org for the Moebius function.
http://www.maa.org/editorial/mathgames/mathgames_11_03_03.html

One item here that was new to me, courtesy of Fred W. Helenius,
was the work Gauss did on this function for his work /Disquisitiones
Arithmeticae/. There is a nice sequence there, apparently not in
OEIS yet.

1, 2, 5, 8, 23, 26, 68, 57, 139, 174, 123, 222, 328, 257, 612,
636, 886, 488, 669, 1064, 876, 1105, 1744, 1780, 1552, 2020,
1853, 2890, 1962, 2712, 2413, 3536, 4384, 3335, 5364, 3322,
3768, 4564, 7683, 7266, 8235, 4344, 8021, 6176, 8274, 6965,
5698, 7581, 13167, 8244.

Sums of primitive roots of primes. Gauss proved:
Sum of primitive roots of prime p ? µ(/p/-1) (mod /p/)

For 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, the primitive roots
are as follows:
{{1}, {2}, {2, 3}, {3, 5}, {2, 6, 7, 8}, {2, 6, 7, 11},
{3, 5, 6, 7, 10, 11, 12, 14}, {2, 3, 10, 13, 14, 15},
{5, 7, 10, 11, 14, 15, 17, 19, 20, 21},
{2, 3, 8, 10, 11, 14, 15, 18, 19, 21, 26, 27}}

PrimitiveRootQ[a_Integer, p_Integer] :=
Block[{fac, res},
fac = FactorInteger[p - 1];
res = Table[PowerMod[a, (p - 1)/fac[[i, 1]], p],
{i, Length[fac]}]; ! MemberQ[res, 1]]

PrimitiveRoots[p_Integer] := Select[Range[p - 1], PrimitiveRootQ[#, p] &]

--Ed Pegg Jr