\(140\mathbf{\color{blue}{\;=\;}}14+15+16+17+18+19+20+21\mathbf{\color{blue}{\;=\;}}17+18+19+20+21+22+23\mathbf{\color{blue}{\;=\;}}26+27+28+29+30\)

\(\qquad~~~~\)(som van opeenvolgende gehele getallen)

\(140\mathbf{\color{blue}{\;=\;}}14+16+18+20+22+24+26\mathbf{\color{blue}{\;=\;}}24+26+28+30+32\mathbf{\color{blue}{\;=\;}}32+34+36+38\)

\(\qquad~~~~\)(som van opeenvolgende pare getallen)

\(140\mathbf{\color{blue}{\;=\;}}5+7+9+11+13+15+17+19+21+23\mathbf{\color{blue}{\;=\;}}69+71\) (som van opeenvolgende onpare getallen)

\(140=5*(1+2+3+4+5+6+7)\) (vijf maal de som van opeenvolgende gehele getallen)

\(140\mathbf{\color{blue}{\;=\;}}1^2+2^2+3^2+4^2+5^2+6^2+7^2\mathbf{\color{blue}{\;=\;}}1+4+9+16+25+36+49\)

\(\qquad~~~~\)(som van de kwadraten van opeenvolgende gehele getallen)

\(140=((0;2;6;10)\,(1;3;3;11)\,(1;3;7;9)\,(2;6;6;8)\,(3;5;5;9))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#5\}\)

\(140=((0;0;1;1;1;1;2;4;4)\,(0;2;2;2;2;3;3;3;3)\,(1;1;1;1;1;1;1;2;5)\,(1;2;2;2;2;2;2;3;4))\lower2pt{\Large{\color{teal}{➌}}}\to\{\#4\}\)

\(140=(1+4+0+1^3+4^3+0^3)*2\)

\(140\mathbf{\color{blue}{\;=\;}}[6^4][36^2]-34^2\mathbf{\color{blue}{\;=\;}}12^2-2^2\)

140.1

\(140\mathbf{\color{blue}{\;=\;}}\)(som van drie derdemachten)

\(\qquad~~~~\)References Sum of Three Cubes

\(\qquad~~~~\)Getallen van de vorm \(~9m+4~\) of \(~9m+5~\) kunnen nooit als som van drie derdemachten geschreven worden.

\(\qquad~~~~\)In dit geval is \(m=15~~(+5)\).

\(140\mathbf{\color{blue}{\;=\;}}\)(som van vier derdemachten)

\(\qquad~~~~(z\gt1000)\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-1)^3+2^3+2^3+5^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+(-7)^3+(-13)^3+14^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-1)^3+(-10)^3+(-19)^3+20^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{17^3+(-34)^3+(-37)^3+44^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+23^3+44^3+(-46)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{8^3+(-19)^3+(-46)^3+47^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{11^3+41^3+50^3+(-58)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-34)^3+(-34)^3+(-79)^3+83^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{47^3+(-67)^3+(-76)^3+86^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{20^3+(-31)^3+(-85)^3+86^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{50^3+(-67)^3+(-88)^3+95^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-31)^3+(-58)^3+(-100)^3+107^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-16)^3+(-31)^3+(-106)^3+107^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-31)^3+(-79)^3+(-127)^3+137^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-1)^3+104^3+116^3+(-139)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{71^3+80^3+122^3+(-139)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{29^3+(-121)^3+(-130)^3+158^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-31)^3+59^3+170^3+(-172)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-43)^3+95^3+176^3+(-184)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{50^3+(-61)^3+(-184)^3+185^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-55)^3+107^3+206^3+(-214)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{149^3+(-169)^3+(-220)^3+230^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-112)^3+(-115)^3+(-217)^3+236^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-91)^3+152^3+224^3+(-241)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{116^3+188^3+227^3+(-271)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-25)^3+158^3+269^3+(-286)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-31)^3+(-157)^3+(-277)^3+293^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-184)^3+(-205)^3+(-223)^3+296^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+(-262)^3+(-265)^3+332^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{98^3+(-109)^3+(-343)^3+344^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-169)^3+(-256)^3+(-334)^3+389^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{137^3+(-292)^3+(-340)^3+395^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-13)^3+224^3+392^3+(-415)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{194^3+269^3+359^3+(-418)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{260^3+(-277)^3+(-415)^3+422^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{344^3+(-382)^3+(-409)^3+437^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-145)^3+(-238)^3+(-406)^3+437^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{158^3+215^3+437^3+(-460)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{323^3+(-343)^3+(-466)^3+476^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-301)^3+350^3+464^3+(-487)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{140^3+407^3+413^3+(-520)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-262)^3+431^3+437^3+(-526)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{101^3+(-211)^3+(-523)^3+533^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-184)^3+386^3+467^3+(-535)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{155^3+(-391)^3+(-508)^3+572^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{71^3+(-310)^3+(-547)^3+578^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{83^3+446^3+473^3+(-580)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{110^3+155^3+578^3+(-583)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{95^3+251^3+623^3+(-637)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-115)^3+470^3+551^3+(-646)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-562)^3+593^3+659^3+(-682)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{470^3+479^3+488^3+(-691)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{347^3+(-604)^3+(-640)^3+761^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{125^3+(-457)^3+(-748)^3+800^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-289)^3+341^3+800^3+(-808)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{173^3+500^3+746^3+(-817)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{296^3+566^3+713^3+(-829)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{269^3+(-280)^3+(-910)^3+911^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{206^3+458^3+869^3+(-913)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{140^3+215^3+917^3+(-922)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-181)^3+(-373)^3+(-925)^3+947^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{536^3+563^3+830^3+(-967)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{209^3+(-754)^3+(-805)^3+980^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{542^3+578^3+845^3+(-985)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-169)^3+563^3+935^3+(-997)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-304)^3+(-382)^3+(-985)^3+1013^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{383^3+(-643)^3+(-964)^3+1034^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{533^3+(-688)^3+(-1000)^3+1055^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-13)^3+776^3+902^3+(-1063)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{137^3+779^3+944^3+(-1096)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{344^3+(-850)^3+(-967)^3+1139^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{623^3+854^3+869^3+(-1150)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{323^3+839^3+977^3+(-1159)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{464^3+869^3+992^3+(-1201)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~(z\gt1000)\)

\(140\mathbf{\color{blue}{\;=\;}}\)(som van vijf vijfdemachten)

\(\qquad~~~~\bbox[3px,border:1px blue solid]{(-1)^5+(-3)^5+26^5+32^5+(-34)^5}\)

140.2
\(140\) als resultaat met breuken waarin de cijfers van \(0\) tot \(9\) exact één keer voorkomen : (\(8\) oplossingen) :
\(257460/1839=273840/1956=415380/2967=461580/3297=\)
\(514920/3678=547680/3912=615720/4398=659820/4713=140\)
140.3

\(140=7!/(3!*3!)\)

140.4

\(140\) is gelijk aan \(28\) maal de som van zijn cijfers : \(140=28*(1+4+0)\)

Andere getallen met dezelfde eigenschap zijn \(112,224,252,280,308,336,364,392,448,476\) en \(588\).

140.5
Men moet \(140\) tot minimaal de \(95613\)ste macht verheffen opdat in de decimale expansie exact \(140\) \(140\)'s verschijnen.
Hier moet een hogere exponent gebruikt worden als normaal want een veelvoud van \(140\) produceert een sliert van
nullen achteraan die nooit een grondtal kunnen herbergen. Terloops : \(140\)\(^{95613}\) heeft een lengte van \(205198\) cijfers.
140.6

\(140^2\mathbf{\color{blue}{\;=\;}}24^3+76^2\mathbf{\color{blue}{\;=\;}}65^3-505^2\mathbf{\color{blue}{\;=\;}}84^2+112^2\mathbf{\color{blue}{\;=\;}}148^2-48^2\mathbf{\color{blue}{\;=\;}}149^2-51^2\mathbf{\color{blue}{\;=\;}}175^2-105^2\mathbf{\color{blue}{\;=\;}}203^2-147^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\;221^2-171^2\mathbf{\color{blue}{\;=\;}}265^2-[15^4][225]\mathbf{\color{blue}{\;=\;}}364^2-336^2\mathbf{\color{blue}{\;=\;}}500^2-480^2\mathbf{\color{blue}{\;=\;}}707^2-693^2\mathbf{\color{blue}{\;=\;}}985^2-975^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\;1085^2-105^3\mathbf{\color{blue}{\;=\;}}1229^2-1221^2\mathbf{\color{blue}{\;=\;}}2452^2-2448^2\mathbf{\color{blue}{\;=\;}}4901^2-4899^2\)

\(140^3\mathbf{\color{blue}{\;=\;}}119^3+1029^2\mathbf{\color{blue}{\;=\;}}329^3-5733^2\mathbf{\color{blue}{\;=\;}}1659^2-91^2\mathbf{\color{blue}{\;=\;}}1680^2-280^2\mathbf{\color{blue}{\;=\;}}1686^2-314^2\mathbf{\color{blue}{\;=\;}}1785^2-665^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\;1872^2-872^2\mathbf{\color{blue}{\;=\;}}1890^2-910^2\mathbf{\color{blue}{\;=\;}}2115^2-1315^2\mathbf{\color{blue}{\;=\;}}2142^2-1358^2\mathbf{\color{blue}{\;=\;}}2310^2-1610^2\mathbf{\color{blue}{\;=\;}}2343^2-1657^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\;2730^2-2170^2\mathbf{\color{blue}{\;=\;}}2994^2-2494^2\mathbf{\color{blue}{\;=\;}}3045^2-2555^2\mathbf{\color{blue}{\;=\;}}3630^2-3230^2\mathbf{\color{blue}{\;=\;}}3696^2-3304^2\mathbf{\color{blue}{\;=\;}}4095^2-3745^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\;5040^2-4760^2\mathbf{\color{blue}{\;=\;}}5613^2-5363^2\mathbf{\color{blue}{\;=\;}}6237^2-6013^2\mathbf{\color{blue}{\;=\;}}6960^2-6760^2\mathbf{\color{blue}{\;=\;}}7098^2-6902^2\mathbf{\color{blue}{\;=\;}}8655^2-8495^2\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\;\bbox[2px,border:1px brown dashed]{9870^2-9730^2} \)

140.7

Als som met de vier operatoren \(+-*\;/\)
\(140=(35+1)+(35-1)+(35*1)+(35/1)\)

140.8
\(140=9*8+7*6+5*4+3*2+1*0\) een pandigitale expressie. 140.9
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
Allemaal Getallen


\(140\)\(2^2*5*7\)\(12\)\(336\)
\(1,2,4,5,7,10,14,20,28,35,70,140\)
\(10001100_2\)\(214_8\)\(8\)C\(_{16}\)
   

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Bewerking & Layout door Patrick De Geest (email)
Laatste update 25 mei 2024