A079201 - OEIS

A079201

Number of isomorphism classes of associative commutative closed binary operations on a set of order n, listed by class size.

1, 1, 0, 3, 0, 0, 3, 9, 0, 0, 0, 3, 0, 0, 16, 39, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 15, 0, 4, 0, 103, 201, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 6, 0, 0, 4, 91, 0, 55, 0, 715, 1258, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12

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OFFSET

0,4

COMMENTS

Number of elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..217 (rows 0..8)

C. van den Bosch, Closed binary operations on small sets

Index entries for sequences related to semigroups

FORMULA

A079194(n,k) + A079197(n,k) + A079200(n,k) + T(n,k) = A079171(n,k).

T(n, A027423(n)) = A058105(n).