Aurifeuillean factors of b^core(b)-(-1)^floor(core(b)/2) for bases b which are not perfect powers (i.e. not in https://oeis.org/A001597), where core(b) is the squarefree part of b (i.e. https://oeis.org/A007913), floor is the floor function.

There are OEIS sequences for specific bases b:

b,L factor,M factor

squarefree b == 1 mod 4,https://oeis.org/A230376,https://oeis.org/A230378

squarefree b == 2 or 3 mod 4,https://oeis.org/A230377,https://oeis.org/A230379

prime b == 1 mod 4,https://oeis.org/A352711,https://oeis.org/A352732

prime b == 3 mod 4,https://oeis.org/A352400,https://oeis.org/A352401

(use the box "Aurifeuillian LMs" in http://myfactorcollection.mooo.com:8090/calculators.html to compute)

b,L factor,M factor

2,1,5

3,1,7

5,11,71

6,13,97

7,113,911

10,3541,27961

11,58367,407353

12,7,19

13,1803647,13993643

14,2826601,19955461

15,19231,142111

17,2699538733,19152352117

18,13,25

19,113631466919,870542161121

20,251,671

21,30778903,227633407

22,9617835527609,73194743542229

23,348275601426959,2498077661567473

24,349,949

26,35522826680397941,255982845098719961

28,13007,35771

29,112663560435723374699,813955076015309926319

30,241498479121,1784464680181

31,8403855868042458448127,63472256064447557254913

33,554945667652531,4098986195943739

34,1161044975606998832441701,8751868368432861971645641

35,1272844589592126671,9227671631659104191

37,6243610407478181159725577611,46959719470144429555105032871

38,10128165505710094110937686497,73515350937824503550370503117

39,4612290807753604561,34089603477374212561

40,1545781,4237021

41,67643278270835231300426724641533,491873569944394295636860313807677

42,11088410788564798837,81914312700762832753

43,7248206084007410402911299180581471,54382651771205224279713471565249817

44,99279247,267860363

45,1471,2851

46,1390229371629213324480602662384989857,10424444935837208726288465136661448813

47,105318477338066161993242388018074119617,767102704711961850109296220485687497279

48,37,61

50,41,61

51,778053427891084736465071399,5749977010265641253803827799

52,12070179083,33018670127

53,253382315888712050791030544452181354268272663,1848593595048531176470116001230356265643249547

54,2089,4069

55,23672289106611457592560839938092561,177048666571753165222942187353147921

56,18758166253,50690605477

57,14710826638296122001733445931451,108685909290746311448943506365699

58,8692693155170789403823958563032406712805848929453,64965712884195911002424367688193729042065260083713

59,830220061043693789623432394289631761145130727636121,6066304600323886604542912453739225327712511596287519

60,7925851,21544711

61,133904013361225746608283522164245432446284642589451147,1000403244183535565720394723140528028235711874491322863

62,218654031962281491558698212468966900181222781058803769,1598199221000104393144295930298581338638609957335261749

63,177451,346837

65,11870972775425394910663203841797074811523441,86820329069666414416574099128599050223826321

66,904928672764804258054289330860660909,6687176121042396611705676048434093689

67,661935119780652835947552219206489357429149541646081291782903,4939550666946228766120378151143880643892475220996412785812081

68,280036765431547,757463413406383

69,10403944608527902936257728314504197407851,76881722531462151387037846863719521437211

70,70151137691304672822761294517994150968111781,523310952733901808694726252398703937437307521

71,22841897842916079359206923988963658063411418453199161599190918287,167216095234951041191120607603910342573638333989428001329719945073

72,61,85

73,4429523820749528526448423858097183945539957285504166342434080091097,33027769942300819203735411144251223948236849608414254057770836237073

74,7243492965458735017277302866784099613876044331952355404960059617349,53046468483771197401105808183426586382295975649305733867845253347849

75,61,91

76,50860037254066463,138864378319793627

77,144372147978218309803568335882418184786765853706180931811,1057506290619700884873376543060518255675559030435525934419

78,946293413157560869042497784958313988327980409,6991759629250150704569077633578317291940902509

79,37032592805942775592027297064629098681015432812873314981288646788880382401,275972688894418789736700752248858100384179398331419102294522495624409089599

80,5021,8261

82,13076000422968591692479950195997785289083599119988185053164292791401705088677,97402180833251915256508474098495503625777489070396371022024849859154539314633

83,1766296380845351227285678245364343387203115679240347429564924470494997630823761,12946095372317349643434751823146435254506683027643658220734050285951563889844887

84,211798114711,575743285531

85,20083440021899068966500578947124501409693267223841467235605261,149566214733275544609454237789423364170125271716411373354822981

86,655062263745396515400787797675339495227668666947676311591250772664328783243769153,4803177172523631963175027896489522816000606501427667769712367486592058930431427757

87,749441159989591741516165399356320668087594910821252879,5537367729326596166072458818384872727818250722456376079

88,16859103484162283741,46000535643921005621

89,22025976442533867023764871677093060750695015730452042650392008772482209127661977853081,161544712910395873343783107708010234888059872104534850810636168827470326009199929377761

90,46950721,91673581

91,12358550804310527670849294676415275031677512137919431333071058859781951,91993922055624263935394800778728797693196991379555322615933009601248591

92,2415255921313278711007,6541448474166217588139

93,41481709864983694013083951011822708328117991031633559816543,306496614934653985768949609076643943320097486428001540389543

94,2128199821358114774921877911308828029159318244144592556640074728094397211681047861057376561,15838023425382156801728525525579612461425661532139912298180939034401658829019119626946912221

95,58553504018554918253790688249923629067839582745242401466452070524472641,429629722366675347891312832012686332479302611673105341076415899508034881

96,7177,11833

97,85411410016592864938535742262164288660754818699519364051241927961077872028620787589587608357877,635434951780516353650912900119894322080826340711500335556434578009638053150509863038991127868733

98,85,113

99,6787552333,13190885467

101,6100420253286674987156224226732428111171759145627478770614902830591800394838498549335390117981792471,44781537243174644742948596601126951496434414405342658654971083700465176803888590639688874168032493531

102,6933302919028307627545618550707065964436703825922599005083107601,51228608402050416908324027962045015358989533036408002418930860821

103,1647815867840765274892930713277013406494133744253819619413929169374533635412743357807881562561883634161,12254402046323271636146357795795593543661856170888200470429292834768655429133340064424574414367685827087

104,972578695177081506417749,2635331421130026749976509

105,1192137880630207335284232749910842896608136907161,8808773677512415004793980650801308641856787484521

106,758957920962929217683784949545285031184330018831867625979626070774343824927045967820516907237732535497741,5643566401997800586493577329970677570885632953335801672049711292496283950656589405781702112889512792941921

107,132551981525557937276747525399826343547912440871359890365374250185068199422063124903322157996864171399661993,973316828722223989818301756298850305460037543217265725884202589573714852250754533372613624587315341929719151

108,91,127

109,38672504747904083216176766692075491704155575493467694491848918021206462129606542614944887231087731672255580899,287516132940242938537556210373976702234092138127284320801003859153080367469335984994265242185635198414045506439

110,1670117243056925773942717890507754806235206109260637733339146742566600507652357941,12266022115368180178937422780266196218786453651059133710063869925025542649023159761

111,15822427460382343817166589155168334269776506898484004784620045104471414049,116916575325814826267318735497853846239923111260791523048258480825003750689

112,1088501,1797293

113,3477894688080783662799978450294453578638114806098679107176218280975064620046412901145663649249419213206000766166961,25546397394379579738891581839811467606086845723469403594741056151805169534176713691918381769864831233404483687818561

114,41142449899137423839733703495205409459158756540150000991458644529060041021,304013285971984007296273616432222610068247390418121548136676270405310616041

115,1725964202735689947226332134086714770591292366841662216626687447464358250729093391369401231,12827390498066239371925581779260309323131247275343662569788439440958111680183085075863163711

116,48726522901359780716652833627,132074332898362838070481057247

117,1844182819987,3598771243783

118,541534091553116270619572935639498095758240772225098795313620557476347387617477892448437423986845911284154400311881778873,4023980393847821582924639722518111060637025180985296406333355759071170947873977329022583521561237589345608618564325838933

119,1566704837906228949659328545620701807786255485108833459172032162069565375295788172677273315593673279,11512122276498623018496922051034358543979058046106269792905220805734605089095323519983372384073417279

120,26080612625600941,70894461235977061

122,56036788334279753878309399987234190943097539482369291559610077746013330453915459369092763475225454168855065191832966245379877,411791394824598785311470789319023223080060169542003820942965132011563366572548149442295035290660871733523287526034774646601193

123,145771913184915601074042275226231758930274922995473994892168182946112800831390370983,1077088531712247051360987745850897307299305535821143594936584907289481265768829982647

124,15200131147938481890512400992687,41429996053914256362412165413563

126,2869630093597,5579474136433

127,1266199938920800466725219654700579769705861846847764788287092927875250613962612461753415717066421872938948107085620433456069520388097,9405032562524437785136871286992594736978186868985359987164387434462590237012328447825708044013234715859329999705024287958405689118719

129,16172545841174713599343199092162369123213516980178728821469252518695822205117552978967691,119502705031522712676185793334881627636384825465765295717113595774933733623323784727292451

130,108114930479460012823960416442979097370848121861448397380118628969264790514928489679834222816910966721,802974669293593799568080093641312542086749056230730386178578239296560889313576565048561145013063712581

131,154094968711068546073229085208466703746302692952484409002535365532232787083819676201861605375998109936383234056651683154095126159807976903,1132862864380040424131249192662601395854547675085555486305249983846541984884017360109747067704141754802968705904768040634365264052424481217

132,970383389135247959719,2637745092164254488571

133,1782262741814873196571901103996012321105552150734659316302754840777590081102224597422536133873455697274870647702791,13235117047106184177706324822482452866517305944678492975991153013809934103598487233836274165462373447638119234908719