Abstract: For any positive integer n,let δ（ｎ） denote the sum of distinct divisors of n.It is proved that there exist infinitely many positive integers n satisfying δ（ｎ）／ｎ＞（ｄ（ａ０）＋ｄ（ａ１）＋…＋ｄ（ａｋ））／（ｋ＋１）,where ai(i=0,1,…,k) are all digits of the decimal notation of n,and d(ai)(i=0,1,…,k) is the divisor function of ai.

Key words: sum of divisors, divisor function, inequality