A129211 Numbers k such that k^3 divides 3^(k^2) - 1.

1, 2, 4, 10, 20, 68, 110, 164, 220, 340, 610, 772, 820, 1010, 1210, 1220, 1510, 2020, 2420, 2530, 2788, 3020, 3740, 3860, 5060, 6710, 7004, 7370, 8020, 9020, 9316, 11110, 11810, 13124, 13420, 13612, 13940, 14740, 16610, 19580, 20740, 20876, 22220

Offset: 1

Author

Alexander Adamchuk, Apr 03 2007

Keywords

• nonn

Links

• Robert Price, Table of n, a(n) for n = 1..249

Crossrefs

Cf. A067945 (numbers k such that k divides 3^k-1).

Cf. A127103 (numbers k such that k^2 divides 3^k-1).

Programs

Mathematica

k=1; Do[ p=Prime[k]; If[ IntegerQ[ (PowerMod[ p+1, n^2, n^3 ] - 1 )/n^3 ], Print[ {k, p, n} ]], {n,1,100000} ]
Join[{1}, Select[Range[3000000], PowerMod[3, #^2, #^3] == 1 &]] (* Robert Price, Mar 31 2020 *)