conjecture: if p is prime, the no. of rings of order p^2 is 11

[Neil Fernandez]

Let a(n) be the number of rings of order p^2, where p is the nth prime.

These are the 4th, 9th, 25th, 49th, etc. terms of A027623.

The sequence begins: 11,11,11,11

And continues?

Interestingly, the known terms of A027623 are only equal to 11 when n is
the square of a prime, so perhaps both the conjecture and its converse
are true.

A027623:
1, 1, 2, 2, 11, 2, 4, 2, 52, 11, 4, 2, 22, 2, 4, 4, 390, 2, 22, 2, 22,
4, 4, 2, 104, 11, 4, 59, 22, 2, 8, 2, ? (>18590), 4, 4, 4, 121, 2, 4, 4,
104, 2, 8, 2, 22, 22, 4, 2, 780, 11, 22, 4, 22, 2, 118, 4, 104, 4, 4, 2,
44, 2, 4, 22, ? (> 829826)

Neil

-- 
Neil Fernandez