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PETER HAGIS, JR
International Journal of Mathematics and Mathematical Sciences, 1988, Letnik: 1988, Številka: 2Journal Article
If the natural number n has the canonical form (The equation is abbreviated) then (The equation is abbreviated) is said to be an exponential divisor of n if b_i|a_i for I = 1, 2,…, r. The sum of the exponential divisors of n is denoted by σ^((e)) (n). n is said to be an e-perfect number if σ^((e)) (n)=2n; (m;n) is said to be an e-amicable pair if σ^((e)) (m)= m+n =σ^((e)) (n); n_0, n_1, n_2,… is said to be an e-aliquot sequence if n_(i+1)=σ^((e)) (n_i)-n_i. Among the results established in this paper are: the density of the e-perfect numbers is .0087; each of the first 10,000,000 e-aliquot sequences is bounded.
