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

1,3

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

Links

Table of n, a(n) for n=1..78.

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.

Example

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

Crossrefs

Cf. A005843, A282572.

A070932 is closely related.

Sequence in context: A141825 A238369 A296858 * A070932 A161577 A358330

Adjacent sequences: A296238 A296239 A296240 * A296242 A296243 A296244

Keyword

nonn

Author

Jonathan Sondow, Dec 14 2017

Status

approved