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A251865
Irregular triangle read by rows in which row n lists the maximal-order elements (<n) mod n.
1
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.
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++)
KEYWORD
nonn,tabf
AUTHOR
Eric Chen, May 20 2015
STATUS
approved