For example, 7 is deficient, since its only proper divisor is 1, which is smaller than 7. It is easy to see that all the primes, their powers and all the semiprimes apart 6, are deficient.
Moreover, if a number is perfect or deficient, then all its proper divisors are deficient.
J.Sándor has proved that for sufficiently large there is always a deficient number between and .
Below, the spiral pattern of deficient numbers up to 2500. See the page on prime numbers for an explanation and links to similar pictures.