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Number of loops of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
0

%I #12 Oct 27 2019 14:34:05

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

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

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

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

%Y Semigroups: A027851 or A001423 (commutative: A001426);

%Y Monoids: A058129 or A058133 (commutative: A058131);

%Y Quasigroups: A057991 or A058171 (commutative: A057992);

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

%Y Groups: A000001 (commutative: A000688);

%Y Rings: A027623 or A038036 (commutative: A037289);

%Y Rings with unity: A037291;

%Y Fields: A069513.

%K nonn,hard,more

%O 0,5

%A _Jianing Song_, Oct 26 2019