Wiki claims that the number 191 is a deficient because 1 is less than 191, but I thought it was deficient because 192 is less than 382. Am I mistaken?

The two definitions are essentially the same. The only difference is whether the number itself as included as one of its own divisors when they are being added up:

- either you take all of the divisors of a number (excluding the number itself) and add them up. If they total less than the number, then it is deficient. For example, the divisors of 10 (excluding 10 itself) are 1, 2, and 5. They add to 8, which is less than 10. 10 is therefore a deficient number.
- or you can take all of the divisors of a number (including the number itself) and add them up. If they total less than twice the number, then it is deficient. For example, the divisors of 10 (including 10 itself) are 1, 2, 5 and 10. They add to 18, which is less than 20. 10 is therefore a deficient number.

So 191 (a prime number) is deficient either because:

1 < 191 or

(1 + 191) < (2 x 191)

That might be clearer if you rephrase the second inequality as

(1 + 191) < (191 + 191) .