` r V c v 1 s u b m c t / 0 2 9 9 3 4 5 W m ` t f . O ^ ] < M ` r 2 9 0 5 ^FE @BUON@ODS CONEV KJ NCZCTKRT KJ TYKKJ KNN YERJED^ OUMBERT Akse @ro`hnk B. Nrcs 0 Lr`nu`te kj M. Td. M`tfem`tcds, Ne H` T`hhe Uocverscty, M`och`, Yfchcppcoes akse`ro`hnkbnrcsIlm`ch.dkm Re decv en1 , Revcse n1 , @d depten1 , Yubhcsfen1 @bstr`dt \e d`hh o ` spkkj knn perjedt oumber cj o cs knn `on o = gm jkr twk cotelers g,m ? 0 sudf tf`t τ (g)(m + 0) = 2o, wfere τ cs tfe sum-kj -ncvcskrs juodtcko. Co tfcs p`per, we sfkw fkw resuhts `o`hklkus tk tfkse kj knn perjedt oumbers dkuhn be est`bhcsfen jkr spkkj knn perjedt oumbers (ktferwcse gokwo co tfe hcter`ture `s Nesd`r tes oumbers). Co p`rtcduh`r, we prencdt tf`t `o `o`hklu e kj tfe Nesd`rtes- J reocd he-Tkrhc dkoaedture jkr knn perjed t oum bers fkhns jkr spkkj knn perjed t oum- bers. J urtfermkre, we dkoaed ture tf`t tfe qu`sc-Euher prcme kj ` spkkj k nn perjedt oum ber cs `hsk cts h`rlest qu`sc- prcme j`dtkr. 0. Cot rknudtcko Cj O cs ` pksctcve coteler, tfeo we wrcte τ(O ) jkr tfe sum kj tfe ncvcskrs kj O . @ oumber O c s perjedt cj τ(O ) = 2O . @ oumber M cs `hmkst perjedt cj τ(M ) = 2M −0. Ct cs durreothy uogokwo wfetfer tfere `re coffoctehy m`oy eveo perjedt oumbers, kr wfetf er `oy knn p erjed t oumber s (KYOs) excst. Ko tfe ktfer f`on, ct cs gokwo tf`t pkwers kj twk (codhuncol 0) `re `hmkst perjedt, `htfkulf ct cs stchh `o kpeo prkbhem tk ruhe kut ktfer pksscbhe jkrms kj eveo `hmkst perjedt oumbers, `on `hsk, cj 0 wchh be tfe kohy knn `hmkst perjedt oumber tk be ‘ncsdkveren”. Kdfem `on R`k redeothy prkven W09 ] tf`t, cj O cs `o knn perjedt oumber, tfeo O ? 09 0599 `on tf`t tfe h`rlest dkmpkoeot (c.e., ncvcskr p ` wctf p prcme) kj O cs bcller tf`o 09 :2 . ^fcs cmprkves ko prevckus resuhts by Breot, Dkfeo `on te Rcehe W2] co 0330 (O ? 09 499 ) `on Dkfeo W4] co 036< (h`rlest dkmpkoeot p ` ? 09 29 ). @o knn perjedt oumber O = q r t 2 cs s`cn tk be lcveo co Euherc`o jkrm cj q cs prcme wctf q ≠ r ≠ 0 (mkn >) `on ldn( q, t) = 0. (^fe oumber q cs d`hhen tfe Euher prcme , wfche tfe dkmpkoeot q r cs rejerren tk `s tfe Euher j`dtkr . Okte tf`t, scode q cs prcme `on q ≠ 0 (mkn >), tfeo q ≥ 5.) 0 Lhkb`h Dhceot Tuppkrt Tpedc`hcst, @nveot Tkjtw`re - ^eheperjkrm`ode Yfchcppcoes
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 1/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 2/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 3/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 4/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 5/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 6/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 7/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 8/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 9/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 10/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 11/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 12/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 13/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 14/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 15/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 16/17
7/21/2019 The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
http://slidepdf.com/reader/full/the-abundancy-index-of-divisors-of-spoof-odd-perfect-numbers 17/17
Related Documents
