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A342377
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Number of rings without 1 containing n elements.
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3
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0, 1, 1, 7, 1, 3, 1, 41, 7, 3, 1, 18, 1, 3, 3, 340, 1, 18, 1, 18, 3, 3, 1, 93, 7, 3, 47, 18, 1, 7, 1
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OFFSET
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1,4
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COMMENTS
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A ring without 1 is still a ring, although sometimes called a rng, or a non-unital ring, or a pseudo-ring (see Wikipedia links).
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LINKS
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FORMULA
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a(p) = 1 if p prime.
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EXAMPLE
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a(1) = 0 because the only ring with 1 element is the zero ring (see link) with the element 0, and for this ring, 0 and 1 coincide.
a(3) = 1 because the Matrix ring with 3 elements with coefficients from Z/3Z:
(0 0) (0 0) (0 0)
0 = (0 0), a = (1 0), b = (2 0)
is without 1 (note this ring is commutative) and there is no other such ring with 3 elements and without 1, hence a(3) = 1.
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CROSSREFS
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Number of rings: A037291 (with 1 containing n elements), this sequence (without 1 containing n elements), A027623 or A037234 (with n elements).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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