%I #13 Feb 16 2020 00:58:58
%S 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
%N Number of prime divisors (counted with multiplicity) of number of rings with n elements.
%C 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.
%H Eric W. Weisstein <a href="http://mathworld.wolfram.com/Ring.html">Ring</a>
%F a(n) = A001222(A027623(n)).
%e 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).
%Y Cf. A001222, A027623.
%K nonn,more,hard
%O 0,7
%A _Jonathan Vos Post_, Feb 05 2011