A328746 Number of loops of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

0, 1, 1, 1, 2, 5, 72, 12151, 53146457

Offset

0,5

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = (A057771(n)+A057996(n))/2.

Crossrefs

For the number of group-like algebraic structures of order n, see:

Semigroups: A027851 or A001423 (commutative: A001426);

Monoids: A058129 or A058133 (commutative: A058131);

Quasigroups: A057991 or A058171 (commutative: A057992);

Loops: A057771 or this sequence (commutative: A089925);

Groups: A000001 (commutative: A000688);

Rings: A027623 or A038036 (commutative: A037289);

Rings with unity: A037291;

Fields: A069513.

Sequence in context: A309366 A007506 A042693 * A172037 A301993 A128297

Adjacent sequences: A328743 A328744 A328745 * A328747 A328748 A328749

Keyword

nonn,hard,more

Author

Jianing Song, Oct 26 2019

Status

approved