A sum-product number is a number n such that the sum of n's digits times the product of n's digit is n itself, for example 135 = (1 + 3 + 5)(1·3·5). Obviously, such a number must be divisible by its digits as well as the sum of its digits. There are only three sum-product numbers: 1, 135, and 144 (OEIS A038369). This can be demonstrated using the following argument due to D. Wilson. Let n be a d-digit sum-product number, and let s and p be the sum and product of its digits. Because n is a d-digit number, we have 10^(d - 1)<=n; s<=9d;p<=9^d.

amenable number | digit | Harshad number