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  • Let m(n) be the number of ordered factorizations of n into factors larger than 1; for example, m(12)=8 (12, 2.6, 6.2, 3.4, 4.3, 2.2.3, 2.3.2, 3.2.2). Denote L=log n and LL=loglog n and let r=1.728... be the solution of zeta(r)=2. We prove that for every e>0 we have for large n the bound m(n) < n^r/exp(L^{1/r}/LL^{1+e}) and that m(n) > n^r/exp(cL^{1/r}/LL^{1/r}) holds for infinitely many n (c>0 is constant).
  • Let m(n) be the number of ordered factorizations of n into factors larger than 1; for example, m(12)=8 (12, 2.6, 6.2, 3.4, 4.3, 2.2.3, 2.3.2, 3.2.2). Denote L=log n and LL=loglog n and let r=1.728... be the solution of zeta(r)=2. We prove that for every e>0 we have for large n the bound m(n) < n^r/exp(L^{1/r}/LL^{1+e}) and that m(n) > n^r/exp(cL^{1/r}/LL^{1/r}) holds for infinitely many n (c>0 is constant). (en)
  • Nechť m(n) je počet uspořádaných faktorizací n na čísla větší než 1, např. m(12)=8 (12, 2.6, 6.2, 3.4, 4.3, 2.2.3, 2.3.2, 3.2.2). Označme L=log n a LL=loglog n a r=1.728... buď řešení rovnice zeta(r)=2. Dokazujeme, že pro každé e>0 pro velké n máme mez m(n) < n^r/exp(L^{1/r}/LL^{1+e}) a že m(n) > n^r/exp(cL^{1/r}/LL^{1/r}) platí pro nekonečně mnoho n (c>0 je konstanta). (cs)
Title
  • On the maximal order of numbers in the 'factorisatio numerorum' problem
  • O maximálním řádu čísel v problému 'factorisatio numerorum' (cs)
  • On the maximal order of numbers in the 'factorisatio numerorum' problem (en)
skos:prefLabel
  • On the maximal order of numbers in the 'factorisatio numerorum' problem
  • O maximálním řádu čísel v problému 'factorisatio numerorum' (cs)
  • On the maximal order of numbers in the 'factorisatio numerorum' problem (en)
skos:notation
  • RIV/00216208:11320/07:00004108!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 470;490
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
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  • 439389
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/07:00004108
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • maximal; order; numbers; 'factorisatio; numerorum'; problem (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [5239C8430D4F]
http://linked.open...i/riv/nazevZdroje
  • Journal of Number Theory
http://linked.open...in/vavai/riv/obor
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 124
http://linked.open...iv/tvurceVysledku
  • Klazar, Martin
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-314X
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  • 11320
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