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Search: id:A118581
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| A118581 |
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Number of nonisomorphic semigroups of order <= n. |
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+0
2
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OFFSET
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0,2
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COMMENT
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Semigroup analogue of A063756 Number of groups 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. This sequence assumes that a semigroup may be empty, and need not have an identity.
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FORMULA
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a(n) = SUM[i=0..n] A027851(i). a(n) = SUM[i=0..n] (2*A001423(i) - A029851(i)).
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EXAMPLE
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a(7) = 1658440 = 1 + 1 + 5 + 24 + 188 + 1915 + 28634 + 1627672.
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CROSSREFS
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Cf. A001329, A001423, A001426, A023814, A027851, A029851, A058108, A063756, A079173.
Sequence in context: A059037 A046907 A091312 this_sequence A102159 A102163 A102164
Adjacent sequences: A118578 A118579 A118580 this_sequence A118582 A118583 A118584
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KEYWORD
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hard,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 07 2006
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