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%I #54 May 12 2024 16:01:18
%S 1,3,5,7,8,11,13,15,17,19,21,23,24,25,29,31,32,33,35,37,40,41,43,47,
%T 51,53,55,56,57,59,61,63,65,67,69,71,73,77,79,80,81,83,85,87,88,89,91,
%U 95,96,97,101,103,104,107,109,113,115,119,120,121,123,127,128
%N Numbers k such that U(i) is not isomorphic to U(k) for all i < k, where U(k) is the multiplicative group of integers modulo k.
%C Numbers k such that A289626(i) < A289626(k) for all i < k.
%C All odd primes are in this sequence. This sequence contains almost all odd numbers.
%C Numbers k divisible by 2 but not by 4 are not members since U(k) is isomorphic to U(k/2) (i.e., 2, 6, 10, 14, ... are not terms).
%C Numbers k divisible by 4 but not by 3 or 8 are not members since U(k) is isomorphic to U(3/4*k) (i.e., 4, 20, 28, 44, ... are not terms).
%C Numbers k divisible by 12 but not by 24 or 36 are not members since U(k) is isomorphic to U(2/3*k) (i.e., 12, 60, 84, 132, ... are not terms).
%C Numbers k divisible by 9 but not by 7 or 27 are not members since U(k) is isomorphic to U(7/9*k) (i.e., 9, 18, 36, 45, 72, ... are not terms).
%C Numbers k divisible by 27 but not by 19 or 81 are not members since U(k) is isomorphic to U(19/27*k) (i.e., 27, 54, 108, 135, ... are not terms).
%C First term == 4 (mod 8) is 252.
%H Jianing Song, <a href="/A296233/b296233.txt">Table of n, a(n) for n = 1..6527</a> (All terms <= 16384.)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n">Multiplicative group of integers modulo n</a>
%F a(n) = min{k : A289626(k) = n}. - _Jianing Song_, Jun 30 2018
%e 75 is not a term because U(55) and U(75) are both isomorphic to C_2 x C_20.
%e 93 is not a term because U(77) and U(93) are both isomorphic to C_2 x C_30.
%e 96 is a term because U(96) is isomorphic to C_2 x C_2 x C_8 and U(k) is not isomorphic to C_2 x C_2 x C_8 for all k < 96.
%o (PARI) isA296233(n) = !(sum(i=1,n-1,znstar(i)[2]==znstar(n)[2])) \\ _Jianing Song_, Oct 04 2018
%Y Cf. A289625, A289626. A319928 is a subsequence.
%K nonn
%O 1,2
%A _Jianing Song_, Apr 29 2018
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