1,2

Monoid analogue of A063756 Number of groups of order <= n. See also A118581 Number of nonisomorphic semigroups of order <= n. A semigroup is an algebraic structure consisting of a set S closed under an associative binary operation (and thus is an associative groupoid). Some sources require that a semigroup have an identity element (in which case semigroups are identical to monoids). Not all sources agree that S should be nonempty. A118581 assumes that a semigroup may be empty, and need not have an identity. This sequence, however, requires an identity, and thus cannot be empty.

a(n) = SUM[i=1..n] A058129(i). a(n) = SUM[i=1..n] (2*A058133(i) - A058132(i)).

Cf. A001329, A001423, A001426, A023814, A027851, A029851, A058108, A058132, A058133, A063756, A079173, A118581.

Sequence in context: A077002 A003704 A000250 this_sequence A005143 A121138 A074508

Adjacent sequences: A118598 A118599 A118600 this_sequence A118602 A118603 A118604

hard,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), May 08 2006