Ok, I'm feeling a bit perplexed now. While fiddling around with this, I decided to create an actual table which contained my set, therefore eliminating the insert in my batch...

--fewer ctes and joins, more functions...

declare @a int, @b-2 int

select @a = 3, @b-2 = 5

;with

gcd (a, b) as...

declare @a int, @b int
select @a = 3, @b = 5
;with
   gcd (a, b) as (select @a, @b union all select b, a % b from gcd where...

declare @a int, @b int
select @a = 3, @b = 5
;with gcd (a, b) as ( select @a, @b union all select b, a % b from gcd where b...

with

r3 (remainder, format) as (select 3, 'Bizz'),

r5 (remainder, format) as (select 5, 'Buzz'),

r15 (remainder, format) as (select 15, 'BizzBuzz'),

...