Some results concerning exponential divisors

Peter Hagis

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-7

Abstract:

If the natural number n has the canonical form p 1 a 1 p 2 a 2 … p r a r then d = p 1 b 1 p 2 b 2 … p r b r 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 ) = 2 n ; ( 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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:861482

DOI: 10.1155/S0161171288000407

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