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

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

1,3

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.

Links

Eric Chen, First 160 rows of triangle, flattened

Eric Chen, First 1000 rows of triangle

Example

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.

Mathematica

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

Prog

(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++)

Crossrefs

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

Sequence in context: A283360 A256366 A046147 * A306196 A052369 A110976

Adjacent sequences: A251862 A251863 A251864 * A251866 A251867 A251868

Keyword

nonn,tabf

Author

Eric Chen, May 20 2015

Status

approved