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

%I A251865 #50 Jun 01 2015 18:24:26
%S A251865 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 A251865 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 A251865 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 A251865 Irregular triangle read by rows in which row n lists the maximal-order elements (<n) mod n.
%C A251865 Conjecture: Triangle contains all nonsquare numbers infinitely many times.
%C A251865 The orders of the numbers in n-th row mod n are equal to A002322(n).
%C A251865 First and last terms of the n-th row are A111076(n) and A247176(n).
%C A251865 Length of the n-th row is A111725(n).
%C A251865 The n-th row is the same as A046147 for n with primitive roots.
%H A251865 Eric Chen, <a href="/A251865/b251865.txt">First 160 rows of triangle, flattened</a>
%H A251865 Eric Chen, <a href="/A251865/a251865.txt">First 1000 rows of triangle</a>
%e A251865 Read by rows:
%e A251865 n     maximal-order elements (<n) mod n
%e A251865 1     0
%e A251865 2     1
%e A251865 3     2
%e A251865 4     3
%e A251865 5     2, 3
%e A251865 6     5
%e A251865 7     3, 5
%e A251865 8     3, 5, 7
%e A251865 9     2, 5
%e A251865 10    3, 7
%e A251865 11    2, 6, 7, 8
%e A251865 12    5, 7, 11
%e A251865 13    2, 6, 7, 11
%e A251865 14    3, 5
%e A251865 15    2, 7, 8, 13
%e A251865 16    3, 5, 11, 13
%e A251865 17    3, 5, 6, 7, 10, 11, 12, 14
%e A251865 18    5, 11
%e A251865 19    2, 3, 10, 13, 14, 15
%e A251865 20    3, 7, 13, 17
%e A251865 etc.
%t A251865 a[n_] := Select[Range[0, n-1], GCD[#, n] == 1 && MultiplicativeOrder[#, n] == CarmichaelLambda[n]& ]; Table[a[n], {n, 1, 36}]
%o A251865 (PARI) c(n)=lcm((znstar(n))[2])
%o A251865 a(n)=for(k=0,n-1,if(gcd(k, n)==1 && znorder(Mod(k,n))==c(n), print1(k, ",")))
%o A251865 n=1; while(n<37, a(n); n++)
%Y A251865 Cf. A111076, A247176, A111725, A046147, A046145, A046146, A046144, A060749, A001918, A071894, A008330.
%K A251865 nonn,tabf
%O A251865 1,3
%A A251865 _Eric Chen_, May 20 2015