D(2n)的密度系数

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D(2n)的密度系数

D(2n)的密度系数与2n的数因子有着密切的关系.表D(2n)=C*2n/ln^2(2n),这时C=∑(1，k_)Cpk.Cpk有时虽然是负的，但是它的极限值且是正的.所以当2n→∞时，Cpk是一个正常数，C=∑(1^，k_)Cpk也是一个正常数，且C*2n/ln^2(2n)→∞.
我们有：2^3=8，D(2^3)=8*0.54050964065797660275049034211751/ln^2(8)=1，3>1;
2^4=16,D(2^4)=16*0.96090602783640284933420505265333/ln^2(16)=2,4>2;
2^5=32,D(2^5)=32*0.75070783424718972604234769738544/ln^2(32)=2,5>2;
2^6=64,D(2^6)=64*1.3512741016449415068762258552937/ln^2(64)=5,6>5;
2^7=128,D(2^7)=128*0.55177025817168444864112555757829/ln^2(128)=3,7>3;
2^8=256,D(2^8)=256*0.96090602783640284933420505265335/ln^2(256)=8,8=8;
2^9=512,D(2^9)=512*0.83610085039280755737966474796301/ln^2(512)=11,9<11;
2^10=1024,D(2^10)=1024*1.0322232720898858733082280839049/ln^2(1024)=22,10<22;
2^11=2048,D(2^11)=2048*0.70965349956179653789940680768463/ln^2(2048)=25,11<25.
当n→∞时，k=o(D(2n)),所以C2=Cp1→a1,a1是一个常数.
C3(6)=0.05461398534319880456108532098148,
C3(12)=-0.02594621914459130089810033407568,
C3(18)=-0.03265615018709559580545950942333,
C3(24)=0.30159724073725324046859971757267
C3(30)=0.30159724073725324046859971757267
C3(36)=0.67613749711654421856615322876966
C3(42)=0.67613749711654421856615322876966
C3(48)=0.81035438105013075978581910259036
C3(54)=0.72262491795135593542393479724326
C3(60)=0.72262491795135593542393479724326
C3(66)=0.72262491795135593542393479724326
C3(72)=0.1728819894833792073344834642376
C3(78)=0.1728819894833792073344834642376
C3(84)=0.1728819894833792073344834642376
C3(90)=0.1728819894833792073344834642376
C3(96)=0.1678188242997454953288573337966
C3(102)=0.1678188242997454953288573337966
C3(108)=0.2726038856151882217468774648536
C3(114)=0.2726038856151882217468774648536
C3(120)=0.2726038856151882217468774648536
C3(126)=0.2726038856151882217468774648536
C3(132)=0.2726038856151882217468774648536
C3(138)=0.2726038856151882217468774648536
C3(144)=1.3349622873773949914843044719084
C3(150)=1.3349622873773949914843044719084
C3(156)=1.3349622873773949914843044719084
当2n→∞时，C3=Cp2,所以Cp2→a2,a2是一个常数.
可知对于所有的Cpk,Cpk→ak,ak是一个常数.
当n→∞时，C2(2^n)<C2(2^n-1),但D(2^n)>D(2^n-1).

4=2^2
C2(4)=0.48045301391820142466710252632669
D(4)=4*0.48045301391820142466710252632669/ln^2(2^2)=1

6=2*3
C2(6)=0.48045301391820142466710252632669
C3(6)=0.05461398534319880456108532098148
D(6)=6*0.53506699926140022922818784730817/ln^2(6)=1

8=2^3
C2(8)=0.54050964065797660275049034211751
D(2^3)=8*0.54050964065797660275049034211751/ln^2(8)=1

10=2*5
C2(10)=0.54050964065797660275049034211751
C5(10)=0.51986998143770299936184293560129
D(10)=10*1.0603796220956796021123332777188/ln^2(10)=2

小草

12=2^2*3
C2(12)=0.54050964065797660275049034211751
C3(12)=-0.02594621914459130089810033407568
D(12)=12*0.51456342151338530185239000804183/ln^2(12)=1

14=2*7
C2(14)=0.54050964065797660275049034211751
C7(14)=0.4544365863414547905567910879152
D(14)=14*0.99494622699943139330728143003271/ln^2(14)=2

16=2^4
C2(16)=0.96090602783640284933420505265333
D(2^4)=16*0.96090602783640284933420505265333/ln^2(16)=2

18=2*3^2
C2(18)=0.96090602783640284933420505265333
C3(18)=-0.03265615018709559580545950942333
D(18)=18*0.92824987764930725352874554323/ln^2(18)=2

20=2^2*5
C2(20)=0.96090602783640284933420505265333
C5(20)=-0.06346484235510645680646837016846
D(20)=20*0.89744118548129639252773668248487/ln^2(20)=2

小草

22=2*11
C2(22)=0.96090602783640284933420505265333
C11(22)=0.34198626059042391046159175565317
D(22)=22*1.3028922884268267597957968083065/ln^2(22)=3

24=2^3*3
C2(24)=0.96090602783640284933420505265333
C3(24)=0.30159724073725324046859971757267
D(24)=24*1.262503268573656089802804770226/ln^2(24)=3

26=2*13
C2(26)=0.96090602783640284933420505265333
C13(26)=0.26392393959447021989138126914537
D(26)=26*1.2248299674308730692255863217987/ln^2(26)=3

28=2^2*7
C2(28)=0.96090602783640284933420505265333
C7(28)=-0.16779267800554779854316171865276
D(28)=28*0.79311334983085505079104333400057/ln^2(28)=2

30=2*3*5
C2(30)=0.96090602783640284933420505265333
C3(30)=0.30159724073725324046859971757267
C5(30)=-0.1056889056711059479248453104618
D(30)=30*1.1568143629025501418779594597642/ln^2(30)=3

小草

32=2^5
C2(32)=0.75070783424718972604234769738544
D(2^5)=32*0.75070783424718972604234769738544/ln^2(32)=2

34=2*17
C2(34)=0.75070783424718972604234769738544
C17(34)=0.71225905393765368316322763752096
D(34)=34*1.4629668881848434092055753349064/ln^2(34)=4

36=2^2*3^2
C2(36)=0.75070783424718972604234769738544
C3(36)=0.67613749711654421856615322876966
D(36)=36*1.4268453313637339446085009261551/ln^2(36)=4

38=2*19
C2(38)=0.75070783424718972604234769738544
C19(38)=-0.05428504111913946691357451155328
D(38)=38*0.69642279312805025912877318583216/ln^2(38)=2

40=2^3*5
C2(40)=0.75070783424718972604234769738544
C5(40)=0.26987953777660522565719772614636
D(40)=40*1.0205873720237949516995454235318/ln^2(40)=3

小草

42=2*3*7
C2(42)=0.75070783424718972604234769738544
C3(42)=0.67613749711654421856615322876966
C7(42)=-0.0963525527505396456040529310175
D(42)=42*1.0205873720237949516995454235318/ln^2(42)=4

44=2^2*11
C2(44)=0.75070783424718972604234769738544
C11(44)=0.22566201930652096276774946311847
D(44)=44*0.97636985355371068881009716050391/ln^2(44)=3

46=2*23
C2(46)=0.75070783424718972604234769738544
C23(46)=0.52394389991889440831483230675136
D(46)=46*1.2746517341660841343571800041368/ln^2(46)=4

48=2^4*3
C2(48)=0.75070783424718972604234769738544
C3(48)=0.81035438105013075978581910259036
D(48)=48*1.5610622152973204858281667999758/ln^2(48)=5

50=2*5^2
C2(50)=0.75070783424718972604234769738544
C5(50)=0.47360608535273543290297808348236
D(50)=50*1.2243139195999251589453257808678/ln^2(50)=4

小草

52=2^2*13
C2(52)=0.75070783424718972604234769738544
C13(52)=0.15000333442372484460881436858012
D(52)=52*0.90071116867091457065116206596556/ln^2(52)=3

54=2*3^3
C2(54)=0.75070783424718972604234769738544
C3(54)=0.72262491795135593542393479724326
D(54)=54*1.4733327521985456614662824946287/ln^2(54)=5

56=2^3*7
C2(56)=0.75070783424718972604234769738544
C7(56)=0.11733446400839908743974775231664
D(56)=56*0.86804229825558881348209544970208/ln^2(56)=3

58=2*29
C2(58)=0.75070783424718972604234769738544
C29(58)=0.38634026519386332581663730945046
D(58)=58*1.1370480994410530518589850068359/ln^2(56)=4

60=2^2*3*5
C2(60)=0.75070783424718972604234769738544
C3(60)=0.72262491795135593542393479724326
C5(60)=0.2030329872212228691690715521282
D(60)=60*1.6763657394197685306353540467569/ln^2(60)=6