Study on Whether a Class of Positive Integers are Anti-sociable Numbers
Sun Shudon · Journal of Changchun University · 2015
Let σ( n) be the sum of all positive integers of positive integern n. If positive integers m and n satisfy σ( n) = σ( m) = m +n,( m,n) is called a pair of amicable numbers. Conversely,for a given positive integern n,if there is not any positive integer m satisfies σ( n) = σ( m) = m + n for n,then n is an anti-sociable number. This paper discusses whether the positive integer Sn=1/2(92n+1) is an anti-sociable number,and proves a conclusion that it is an anti-sociable number,in which n is an any positive integer.