A251865 - OEIS

%I #50 Jun 01 2015 18:24:26

%S 0,1,2,3,2,3,5,3,5,3,5,7,2,5,3,7,2,6,7,8,5,7,11,2,6,7,11,3,5,2,7,8,13,

%T 3,5,11,13,3,5,6,7,10,11,12,14,5,11,2,3,10,13,14,15,3,7,13,17,2,5,10,

%U 11,17,19,7,13,17,19,5,7,10,11,14,15,17,19,20,21,5,7,11,13,17,19,23,2,3,8,12,13,17,22,23

%N Irregular triangle read by rows in which row n lists the maximal-order elements (<n) mod n.

%C Conjecture: Triangle contains all nonsquare numbers infinitely many times.

%C The orders of the numbers in n-th row mod n are equal to A002322(n).

%C First and last terms of the n-th row are A111076(n) and A247176(n).

%C Length of the n-th row is A111725(n).

%C The n-th row is the same as A046147 for n with primitive roots.

%H Eric Chen, <a href="/A251865/b251865.txt">First 160 rows of triangle, flattened</a>

%H Eric Chen, <a href="/A251865/a251865.txt">First 1000 rows of triangle</a>

%e Read by rows:

%e n     maximal-order elements (<n) mod n

%e 1     0

%e 2     1

%e 3     2

%e 4     3

%e 5     2, 3

%e 6     5

%e 7     3, 5

%e 8     3, 5, 7

%e 9     2, 5

%e 10    3, 7

%e 11    2, 6, 7, 8

%e 12    5, 7, 11

%e 13    2, 6, 7, 11

%e 14    3, 5

%e 15    2, 7, 8, 13

%e 16    3, 5, 11, 13

%e 17    3, 5, 6, 7, 10, 11, 12, 14

%e 18    5, 11

%e 19    2, 3, 10, 13, 14, 15

%e 20    3, 7, 13, 17

%e etc.

%t a[n_] := Select[Range[0, n-1], GCD[#, n] == 1 && MultiplicativeOrder[#, n] == CarmichaelLambda[n]& ]; Table[a[n], {n, 1, 36}]

%o (PARI) c(n)=lcm((znstar(n))[2])

%o a(n)=for(k=0,n-1,if(gcd(k, n)==1 && znorder(Mod(k,n))==c(n), print1(k, ",")))

%o n=1; while(n<37, a(n); n++)

%Y Cf. A111076, A247176, A111725, A046147, A046145, A046146, A046144, A060749, A001918, A071894, A008330.

%K nonn,tabf

%O 1,3

%A _Eric Chen_, May 20 2015