On the frequency of $k$-deficient numbers
Jean–Marie De Koninck, Imre Kátai · Publicationes Mathematicae Debrecen · 2002
A number n is said to be k-deficient if σ(n) 1 and a function H(x) satisfying H(x)/(log log log x • log log log log x) → +∞ then, if n is sufficiently large, there is always a k-deficient number between n and n + H(n).