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A279401 Irregular triangle read by rows. Row n gives the orders of the primes of row n of the irregular triangle A279399 modulo A033949(n).

%I A279401 #7 Jan 30 2017 21:46:57
%S A279401 2,2,2,2,2,2,4,4,2,4,4,4,2,4,4,4,4,2,4,4,2,6,6,6,2,6,6,2,2,2,2,2,2,2,
%T A279401 6,6,6,2,6,6,6,4,2,4,4,2,4,2,8,8,4,8,8,2,8,4,8,2,10,10,10,10,10,10,2,
%U A279401 10,5,12,12,3,4,12,6,12,2,6,6,6,6,3,2,2,6,6,6,12,4,12,12,6,12,6,6,4,12,4,4,2,4,4,2,4,2,2,4
%N A279401 Irregular triangle read by rows. Row n gives the orders of the primes of row n of the irregular triangle A279399 modulo A033949(n).
%C A279401 The length of row n is given by A279400(n).
%C A279401 See the A279399 comments.
%C A279401 The entries in row n are proper divisors of phi(A033949(n)), where phi(n) = A000010(n).
%C A279401   This is because no A033949 number has a primitive root.
%F A279401 T(n, k) = order(A279399(n, k)) (mod A033949(n)), n >= 1, k = 1..A279400(n).
%e A279401 The irregular triangle T(n, k) begins (here N = A033949(n)):
%e A279401 n,   N \ k 1  2  3  4  5  6  7  8  9 10 ...
%e A279401 1,   8:    2  2  2
%e A279401 2,  12:    2  2  2
%e A279401 3,  15:    4  4  2  4
%e A279401 4,  16:    4  4  2  4  4
%e A279401 5,  20:    4  4  2  4  4  2
%e A279401 6,  21:    6  6  6  2  6  6
%e A279401 7,  24:    2  2  2  2  2  2  2
%e A279401 8,  28:    6  6  6  2  6  6  6
%e A279401 9,  30:    4  2  4  4  2  4  2
%e A279401 10, 32:    8  8  4  8  8  2  8  4  8  2
%e A279401 11, 33:   10 10 10 10 10 10  2 10  5
%e A279401 12, 35:   12 12  3  4 12  6 12  2  6
%e A279401 13, 36:    6  6  6  3  2  2  6  6  6
%e A279401 14, 39:   12  4 12 12  6 12  6  6  4 12
%e A279401 15, 40:    4  4  2  4  4  2  4  2  2  4
%e A279401 ...
%e A279401 The sequence of phi(N) begins: 4, 4, 8, 8, 8, 12, 8, 12, 8, 16, 20, 24, 12, 24, 16, ...
%e A279401 n = 2, N = 12:  5^2 == 7^2 == 11^2 == 1 (mod 12), therefore 2 is the least positive power k for each of the three primes p of row 2 of A279399 which satisfies p^k == 1 (mod A033949(2)).
%Y A279401 Cf. A000010, A033949, A279399, A279400.
%K A279401 nonn,tabf
%O A279401 1,1
%A A279401 _Wolfdieter Lang_, Jan 30 2017