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%I #28 Dec 25 2021 06:55:48
%S 0,1,2,3,4,6,7,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,31,32,34,
%T 36,38,40,42,44,45,46,48,49,50,52,54,56,58,60,62,63,64,66,68,70,72,74,
%U 76,78,80,81,82,84,86,88,90,92,93,94,96,98,100,102,104,105,106,108,110,112,114,116,118,120,122,124,126
%N Finite number of units in a commutative ring; nonnegative even numbers together with products of Mersenne numbers.
%C Zero together with orders of finite abelian groups that appear as the group of units in a commutative ring (Chebolu and Lockridge).
%C Equals A005843 union A282572.
%C Also the possible number of units in a (commutative or non-commutative) ring, since every odd number that is the number of units of a ring must be in this sequence (Ditor's theorem, stated in the S. Chebolu and K. Lockridge link). - _Jianing Song_, Dec 24 2021
%H S. Chebolu and K. Lockridge, <a href="http://dx.doi.org/10.4169/amer.math.monthly.124.10.960">How Many Units Can a Commutative Ring Have?</a>, Amer. Math. Monthly, 124 (2017), 960-965; <a href="https://arxiv.org/abs/1701.02341">arXiv</a>, arXiv:1701.02341 [math.AC], 2017.
%e The even integers {0, +-2, +-4, ...} form a commutative ring with no (multiplicative) units, so a(1) = 0.
%Y Cf. A005843, A282572.
%Y A070932 is closely related.
%K nonn
%O 1,3
%A _Jonathan Sondow_, Dec 14 2017
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