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A127103
Numbers k such that k^2 divides 3^k-1.
28
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
From Alexander Adamchuk, Jan 11 2007: (Start)
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,...}. (End)
LINKS
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 *)
PROG
(PARI) is(k) = Mod(3, k^2)^k == 1; \\ Amiram Eldar, May 21 2024
CROSSREFS
Subset of A067945 (numbers k that divide 3^k - 1).
Sequence in context: A110371 A120388 A061348 * A059831 A064493 A145614
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Jan 05 2007
EXTENSIONS
More terms from Ryan Propper and Alexander Adamchuk, Jan 05 2007
STATUS
approved