journal6 ›› 2007, Vol. 28 ›› Issue (5): 11-12.

• Mathematics • Previous Articles     Next Articles

An Inequality on the Arithmetic Function δ(n)


  1. (Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China)
  • Online:2007-09-25 Published:2012-06-11

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

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