Numbers n such that 3^n-1 has only one primitive prime factor.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 20, 21, 24, 26, 32, 33, 36, 40, 46, 60, 63, 64, 70, 71, 72, 86, 103, 108, 128, 130, 132, 143, 145, 154, 161, 236, 255, 261, 276, 279, 287, 304, 364, 430, 464, 513, 528, 541, 562, 665, 672, 680, 707, 718, 747, 760
1
Numbers n such that S000001(n) = 1.
T. D. Noe, Plot of 130 terms
T. D. Noe, Table of 130 terms
Eric W. Weisstein, MathWorld: Primitive Prime Factor
(Mma) d = 3; Select[Range[1000], PrimePowerQ[Cyclotomic[#, d]/GCD[Cyclotomic[#, d], #]] &]
Cf. A161508 (2^n-1 case), S000001, S000361-S000366.
nonn,hard
T. D. Noe, Nov 20 2014