A318411 - OEIS

%I #40 Sep 02 2018 04:30:14

%S 2,3,5,3,7,5,11,13,7,5,17,19,7,11,23,13,29,5,31,11,17,13,37,19,13,41,

%T 7,43,23,47,17,53,21,19,29,59,61,31,13,11,67,23,13,71,73,37,31,13,79,

%U 41,83,17,43,29,89,13,31,47,37,97,101,17,103,13,53,107,109,21,37,113,19

%N Least k (>1) such that m^k == m mod A005117(n) for 0 <= m <= A005117(n) - 1.

%C This sequence is different from A073482.

%H Seiichi Manyama, <a href="/A318411/b318411.txt">Table of n, a(n) for n = 2..10000</a>

%e A005117(5) = 6.

%e     0^3  =   0 == 0 mod 6,

%e     1^3  =   1 == 1 mod 6,

%e     2^3  =   8 == 2 mod 6,

%e     3^3  =  27 == 3 mod 6,

%e     4^3  =  64 == 4 mod 6,

%e     5^3  = 125 == 5 mod 6.

%e ------------------------------------------------

%e A005117(23) = 35.

%e     0^13 =                    0 ==  0 mod 35,

%e     1^13 =                    1 ==  1 mod 35,

%e     2^13 =                 8192 ==  2 mod 35,

%e    ...

%e    34^13 = 81138303245565435904 == 34 mod 35.

%e ------------------------------------------------

%e ------+------------+------

%e    n  | A005117(n) | a(n)

%e ------+------------+------

%e     2 |          2 |    2

%e     3 |          3 |    3

%e     4 |          5 |    5

%e     5 |          6 |    3

%e     6 |          7 |    7

%e     7 |         10 |    5

%e     8 |         11 |   11

%e     9 |         13 |   13

%e    10 |         14 |    7

%e    11 |         15 |    5

%e    12 |         17 |   17

%e    13 |         19 |   19

%e    14 |         21 |    7

%e    15 |         22 |   11

%e    16 |         23 |   23

%e    17 |         26 |   13

%e    18 |         29 |   29

%e    19 |         30 |    5

%e    20 |         31 |   31

%e    21 |         33 |   11

%e    22 |         34 |   17

%e    23 |         35 |   13

%Y Cf. A005117, A318572.

%K nonn

%O 2,1

%A _Seiichi Manyama_, Aug 26 2018