It is known that the
natural density of such numbers is 1: indeed, the proportion of numbers less than
X which are not arithmetic is
asymptotically :\exp\left( { -c \sqrt{\log\log X} } \,\right) where
c = 2 + o(1). A number
N is arithmetic if the
number of divisors d(
N) divides the
sum of divisors σ(
N). It is known that the
density of integers
N obeying the stronger condition that
d(
N)2 divides σ(
N) is 1/2. ==Notes==