

A185894


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


0



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
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OFFSET

0,7


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..32.
Eric W. Weisstein Ring


FORMULA

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


EXAMPLE

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).


CROSSREFS

Cf. A001222, A027623.
Sequence in context: A327518 A174532 A089242 * A214180 A343073 A184166
Adjacent sequences: A185891 A185892 A185893 * A185895 A185896 A185897


KEYWORD

nonn,more,hard


AUTHOR

Jonathan Vos Post, Feb 05 2011


STATUS

approved



