*I asked this on Math.SE but got no answer:*

Here I read about a variant on the Ulam spiral:

[A] structure may be seen when composite numbers are also included in the Ulam spiral. [...] Using the size of the dot representing an integer to indicate the number of factors and coloring prime numbers red and composite numbers blue produces the figure shown.

The figure below is the resulting spiral:

**Questions:**

Is it surprising that there are thick diagonals? (Stated in the same manner as is stated about the original one,) is it surprising that there are quadratics which generate surprisingly large number of composites with many divisors? Isn't there a simple explanation?

How exactly do the variant and the original spirals relte? Thinking only about the dots and not their colors, the primes and the composites with very few divisors are not distinguishable in the variant.

Thanks in advance.