A296241 Finite number of units in a commutative ring; nonnegative even numbers together with products of Mersenne numbers.

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

Offset: 1

Author

Jonathan Sondow, Dec 14 2017

Keywords

• nonn

Comments

Zero together with orders of finite abelian groups that appear as the group of units in a commutative ring (Chebolu and Lockridge).

Equals A005843 union A282572.

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

Examples

			The even integers {0, +-2, +-4, ...} form a commutative ring with no (multiplicative) units, so a(1) = 0.
		

Links

• S. Chebolu and K. Lockridge, How Many Units Can a Commutative Ring Have?, Amer. Math. Monthly, 124 (2017), 960-965; arXiv, arXiv:1701.02341 [math.AC], 2017.

Crossrefs

Cf. A005843, A282572.

A070932 is closely related.