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A296241
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Finite number of units in a commutative ring; nonnegative even numbers together with products of Mersenne numbers.
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3
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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, 36, 38, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 56, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 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
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OFFSET
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1,3
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COMMENTS
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Zero together with orders of finite abelian groups that appear as the group of units in a commutative ring (Chebolu and Lockridge).
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
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LINKS
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EXAMPLE
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The even integers {0, +-2, +-4, ...} form a commutative ring with no (multiplicative) units, so a(1) = 0.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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