

A305858


a(n) = number of nearrings with n elements.


1



1, 3, 5, 35, 10, 99, 24, 3858, 486, 535, 139, 54694, 454
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OFFSET

1,2


COMMENTS

Nearrings are defined like rings but addition need not be commutative and multiplication need only leftdistribute over addition (of course, rightdistribution leads to an equivalent theory). Also, there need not exist a multiplicative identity.


REFERENCES

Gunter Pilz, NearRings: The Theory and its Applications, Revised Edition (1983), NorthHolland Publishing Company.


LINKS



FORMULA

Since all rings are nearrings, a(n) >= A027623(n).


EXAMPLE

The only nearring of order 1 is the trivial ring, so a(1) = 1.
There are 3 nearrings of order 2, all over Z2, so a(2) = 3.
There are 5 nearrings of order 3, all over Z3, so a(3) = 5.
There are 12 nearrings over Z4 and 23 nearrings over Z2^2, so a(4) = 12 + 23 = 35.
There are 10 nearrings of order 5, all over Z5, so a(5) = 10.
There are 60 nearrings over Z6 and 39 nearrings over S3, so a(6) = 60 + 39 = 99.
There are 24 nearrings of order 7, all over Z7, so a(7) = 24.
There are 135 nearrings over Z8, 1447 nearrings over D8, 281 nearrings over Q, 115 over Z4*Z2, and many over Z2^3, so a(8) > 1978.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



