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

0,7

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: A089242 A349258 A349326 * A376305 A214180 A343073

Adjacent sequences: A185891 A185892 A185893 * A185895 A185896 A185897

Keyword

nonn,more,hard

Author

Jonathan Vos Post, Feb 05 2011

Status

approved