A127103 Numbers n such that n^2 divides 3^n-1.

1, 2, 4, 20, 220, 1220, 2420, 5060, 13420, 14740, 23620, 55660, 145420, 147620, 162140, 237820, 259820, 290620, 308660, 339020, 447740, 847220, 899140, 1210220, 1440820, 1599620, 1759340, 2332660, 2616020, 2858020, 3196820, 3344660

Offset

1,2

Comments

a(n) is a subset of A067945(n) = {1, 2, 4, 8, 16, 20, 32, 40, 64, 80, 100, 128, 160, 200, 220, ...} Numbers n such that n divides 3^n-1.

2 divides a(n) for n>1. 2^2 divides a(n) for n>2. 5 divides a(n) for n>3. 11 divides a(n) for n = {5,7,8,9,10,12,13,14,15,16,17,18,19,20,22,23,24,26,27,28,29,30,31,31,33,34,35,...}. 11^2 divides a(n) for n = {7,12,14,15,26,27,29,30,31,33,34,...}. Prime factors of a(n) in order of their appearance in a(n) are {2,5,11,61,23,67,1181,661,47,1321,367,3851,5501,727,461,269,...}. - Alexander Adamchuk, Jan 11 2007

Links

Table of n, a(n) for n=1..32.

Mathematica

Select[Range[30000], IntegerQ[(PowerMod[3, #, #^2 ]-1)/#^2 ]&]
Join[{1}, Select[Range[335*10^4], PowerMod[3, #, #^2]==1&]] (* Harvey P. Dale, Oct 02 2019 *)

Crossrefs

Cf. A127100, A127101, A127102, A127104, A123105, A127106, A127107, A127092. Cf. A067945 = numbers n such that n divides 3^n-1.

Sequence in context: A110371 A120388 A061348 * A059831 A064493 A145614

Adjacent sequences: A127100 A127101 A127102 * A127104 A127105 A127106

Keyword

nonn

Author

Alexander Adamchuk, Jan 05 2007

Extensions

More terms from Ryan Propper and Alexander Adamchuk, Jan 05 2007

Status

approved