In number theory, an arithmetic number is an integer for which the arithmetic mean of its positive divisors, is an integer. The first numbers in the sequence are 1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20 (sequence A003601 in OEIS). 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
where c = 2 √ log 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 for which d(N)2 divides σ(N) is 1/2.