A027623 -id:A027623 - cp's OEIS frontend

A185894 Number of prime divisors (counted with multiplicity) of number of rings with n elements.

0, 0, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 2, 4, 1, 2, 2, 1, 2, 2, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1

Offset: 0

Jonathan Vos Post, Feb 05 2011

By convention, there is 1 ring with no elements. The first value that I don't know is a(32), where the number of rings with 32 elements was said by Christof Noebauer in 2000 to be > 18590. The next value not known to me is a(64), which is where the same source gives the number of rings with 64 elements > 829826. The articles by Christof Noebauer are linked to from A027623.

			a(16) = 4 because there are A027623(16) = 390 rings with 16 elements, and 390 = 2 * 3 * 5 * 13 has 4 prime divisors counted with multiplicity (in this example, each has multiplicity of 1).

Eric W. Weisstein Ring

Cf. A001222, A027623.

a(n) = A001222(A027623(n)).

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

Original entry on oeis.org

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

Offset: 0

Jianing Song, Oct 26 2019

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.

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

cp's OEIS Frontend

A185894 Number of prime divisors (counted with multiplicity) of number of rings with n elements.

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