Some results concerning exponential divisors
If the natural number n has the canonical form p1a1p2a2…prar then d=p1b1p2b2…prbr is said to be an exponential divisor of n if bi|ai 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 pai...
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000407 |
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| author | Peter Hagis |
| author_facet | Peter Hagis |
| author_sort | Peter Hagis |
| collection | DOAJ |
| description | If the natural number n has the canonical form p1a1p2a2…prar then d=p1b1p2b2…prbr is said to be an exponential divisor of n if bi|ai 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); n0,n1,n2,… is said to be an e-aliquot sequence if ni+1=σ(e)(ni)−ni. Among the results established in this paper are: the density of the e-perfect numbers is .0087; each of the first 10,000,000e-aliquot sequences is bounded. |
| format | Article |
| id | doaj-art-86ac1c53483e42ffb832627a0c87e823 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-86ac1c53483e42ffb832627a0c87e8232025-02-03T01:03:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111234334910.1155/S0161171288000407Some results concerning exponential divisorsPeter Hagis0Mathematics Department, Temple University, Philadelphia 19122, PA, USAIf the natural number n has the canonical form p1a1p2a2…prar then d=p1b1p2b2…prbr is said to be an exponential divisor of n if bi|ai 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); n0,n1,n2,… is said to be an e-aliquot sequence if ni+1=σ(e)(ni)−ni. Among the results established in this paper are: the density of the e-perfect numbers is .0087; each of the first 10,000,000e-aliquot sequences is bounded.http://dx.doi.org/10.1155/S0161171288000407exponential divisorse-perfect numberse-amicable numberse-aliquot sequences. |
| spellingShingle | Peter Hagis Some results concerning exponential divisors International Journal of Mathematics and Mathematical Sciences exponential divisors e-perfect numbers e-amicable numbers e-aliquot sequences. |
| title | Some results concerning exponential divisors |
| title_full | Some results concerning exponential divisors |
| title_fullStr | Some results concerning exponential divisors |
| title_full_unstemmed | Some results concerning exponential divisors |
| title_short | Some results concerning exponential divisors |
| title_sort | some results concerning exponential divisors |
| topic | exponential divisors e-perfect numbers e-amicable numbers e-aliquot sequences. |
| url | http://dx.doi.org/10.1155/S0161171288000407 |
| work_keys_str_mv | AT peterhagis someresultsconcerningexponentialdivisors |