## S000549

Number of primitive roots that are minimal.

1, 2, 4, 6, 8, 12, 16, 18, 32, 36, 40, 48, 54, 72, 80, 84, 96, 120, 144, 160, 162, 200, 216, 240, 288, 320, 336, 384, 432, 448, 480, 576, 720, 768, 880, 960, 1056, 1200, 1280, 1344, 1440, 1458, 1680, 1728, 1920, 2112, 2208, 2304, 2400, 2592, 2784, 2880, 3072, 3456, 3840

1

There are a finite number of numbers having n primitive roots. Sequence S000550 gives the last number having a given number of these primitive roots. Sequence S000551 is an irregular triangle listing the numbers that have a given number of these primitive roots.

T. D. Noe, Plot of 55 terms

Eric W. Weisstein, MathWorld: Primitive Root

(Mma) nn=10000; t = Join[{1}, Table[pr = PrimitiveRootList[n]; Length[pr], {n, 2, 50000}]]; mn = Infinity; mnLst = {}; Do[If[0 < t[[n]] < mn, mn = t[[n]]; AppendTo[mnLst, mn]], {n, nn, 1, -1}]; mnLst = Select[Reverse[mnLst], # < 0.08*nn &]

Cf. A046144, S000550, S000551, S000552.

nonn

T. D. Noe, Mar 25 2015

© Tony D Noe 2014-2015