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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 (list; graph; refs; listen; history; text; internal format)
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) =  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: A228098 A174532 A089242 * A214180 A184166 A029423

Adjacent sequences:  A185891 A185892 A185893 * A185895 A185896 A185897

KEYWORD

nonn,more,hard

AUTHOR

Jonathan Vos Post, Feb 05 2011

STATUS

approved

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Last modified December 3 18:47 EST 2016. Contains 278745 sequences.