A251865 Irregular triangle read by rows in which row n lists the maximal-order elements (

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, 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, 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

Offset: 1

Author

Eric Chen, May 20 2015

Keywords

• nonn
• tabf

Comments

Conjecture: Triangle contains all nonsquare numbers infinitely many times.

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

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

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

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

Examples

			Read by rows:
n     maximal-order elements (<n) mod n
1     0
2     1
3     2
4     3
5     2, 3
6     5
7     3, 5
8     3, 5, 7
9     2, 5
10    3, 7
11    2, 6, 7, 8
12    5, 7, 11
13    2, 6, 7, 11
14    3, 5
15    2, 7, 8, 13
16    3, 5, 11, 13
17    3, 5, 6, 7, 10, 11, 12, 14
18    5, 11
19    2, 3, 10, 13, 14, 15
20    3, 7, 13, 17
etc.
		

Links

• Eric Chen, First 160 rows of triangle, flattened
• Eric Chen, First 1000 rows of triangle

Crossrefs

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

Programs

Mathematica

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

PARI

c(n)=lcm((znstar(n))[2])
a(n)=for(k=0,n-1,if(gcd(k, n)==1 && znorder(Mod(k,n))==c(n), print1(k, ",")))
n=1; while(n<37, a(n); n++)