\(118=28+29+30+31\) (som van opeenvolgende gehele getallen)

\(118=58+60\) (som van opeenvolgende pare getallen)

\(118=((0;1;6;9)\,(0;3;3;10)\,(1;1;4;10)\,(1;2;7;8)\,(2;4;7;7)\,(2;5;5;8)\,(3;3;6;8))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#7\}\)

\(118\mathbf{\color{blue}{\;=\;}}\bbox[#f4f4f4,3px,border:1px solid]{3^3+3^3+4^3}\mathbf{\color{blue}{\;=\;}}((0;0;0;0;0;0;3;3;4)\,(0;0;1;1;2;3;3;3;3)\,(0;1;1;1;2;2;2;3;4))\lower2pt{\Large{\color{teal}{➌}}}\to\{\#3\}\)

\(118=3^3+3^3+2^6\)

\(118\mathbf{\color{blue}{\;=\;}}\bbox[tan,3px]{3^5-5^3}\mathbf{\color{blue}{\;=\;}}7^3-15^2\mathbf{\color{blue}{\;=\;}}19^2-3^5\)

118.1

\(118\mathbf{\color{blue}{\;=\;}}\)(som van drie derdemachten)

\(\qquad~~~~36\) oplossingen bekend

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

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

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

\(\qquad~~~~\bbox[3px,border:1px solid]{3^3+(-5)^3+6^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{25^3+40^3+(-43)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-41^3+(-46)^3+55^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{76^3+81^3+(-99)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-92)^3+(-205)^3+211^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{87^3+207^3+(-212)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{122^3+241^3+(-251)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{217^3+469^3+(-484)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-311)^3+(-1051)^3+1060^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-797)^3+(-1142)^3+1259^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{2484^3+2607^3+(-3209)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{383^3+4327^3+(-4328)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-8318)^3+(-35687)^3+35837^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{27848^3+35101^3+(-40175)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{62856^3+106555^3+(-113397)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-177859)^3+(-508538)^3+515689^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{966222^3+1536861^3+(-1654871)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{2574827^3+3359032^3+(-3802277)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{2918068^3+4215149^3+(-4637567)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-1648978)^3+(-9075473)^3+9093583^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{3442206^3+11808921^3+(-11905619)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{9086157^3+56372193^3+(-56450768)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-84439029)^3+(-285408446)^3+287851107^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-217885004)^3+(-1084880891)^3+1087802537^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{419419465^3+2720474149^3+(-2723793136)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-1808773713)^3+(-6140815052)^3+6192685047^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-6251351521)^3+(-7535365898)^3+8759777791^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-31285384691)^3+(-32726125479)^3+40345142262^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{27124733759)^3+49828145023^3+(-52375070162)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{1491542593332^3+2948502861435^3+(-3070604628725)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-1378365463857)^3+(-5818399773665)^3+5844071201946^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-17314968337937)^3+(-33692026981705)^3+35152197899716^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-46811643649815)^3+(-58844440655726)^3+67411482058989^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px solid]{(-55110113457439)^3+(-362394669898304)^3+362818996874701^3}\mathbf{\color{blue}{\;=\;}}\)

\(118\mathbf{\color{blue}{\;=\;}}\)(som van vijf vijfdemachten)

\(\qquad~~~~(z\gt200)\)

\(\qquad~~~~\bbox[3px,border:1px blue solid]{(-335)^5+623^5+868^5+887^5+(-1025)^5}\)

\(\qquad~~~~\bbox[3px,border:1px blue solid]{(-430)^5+(-490)^5+(-1439)^5+(-1566)^5+1733^5}\)

118.2

\(118\) kan op vier wijzen in een som van drie getallen worden opgesplitst, zó dat in de vier gevallen het product van de
getallen steeds hetzelfde is :

\begin{align} 14+50+54&&=&&15+40+63&&=&&18+30+70&&=&&21+25+72&\qquad(=118)\\ 14\,*\,50\,*54\,&&=&&15\,*\,40\,*\,63&&=&&18\,*\,30\,*\,70&&=&&21\,*\,25\,*\,72&\qquad(=37800) \end{align}

Zie bij voor een opsplitsing op drie verschillende wijzen.

118.3
\(118\) als resultaat met breuken waarin de cijfers van \(0\) tot \(9\) exact één keer voorkomen : (\(1\) oplossing) :
\(952614/8073=118\) 		118.4
Men moet \(118\) tot minimaal de \(43476\)ste macht verheffen opdat in de decimale expansie exact \(118\) \(118\)'s verschijnen.
Terloops : \(118\)\(^{43476}\) is \(90078\) cijfers lang. Noteer dat \(43476\) en \(90078\) exact één keer voorkomen in de decimale expansie. 		118.5

\(118^2\mathbf{\color{blue}{\;=\;}}10^2+24^3\mathbf{\color{blue}{\;=\;}}3482^2-3480^2\)

\(118^3\mathbf{\color{blue}{\;=\;}}193^3-2355^2\mathbf{\color{blue}{\;=\;}}3599^2-3363^2\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{7021^2-6903^2}\mathbf{\color{blue}{\;=\;}}\ldots\mathbf{\color{blue}{\;=\;}}410759^2-410757^2\)

118.6

Expressie met tweemaal de cijfers uit het getal \(118\) enkel met operatoren \(+,-,*,/,(),\)^^\(\)
\(118=(1+1+8)*(1\)^^\(1)+8\)

118.7

Voor \(n=118~~\) geldt \(~~{\large\sigma}(n)={\large\sigma}(n+27) ~~\to~~ {\large\sigma}(118)={\large\sigma}(145)=180~~~~({\large\sigma}\) of  'sigma' staat voor som der delers)

\(118\) is de derde oplossing uit de reeks \(42,48,118,138,1338,3438,8618,\ldots\)

118.8

\(118!!-1~~\)is een priemgetal van \(98\) cijfers lang (\(79945374848\ldots9999999999\)). (OEIS A007749) (Dubbelfaculteit)

Pari/GP code : isprime(prod(i=1,118/2,2*i)-1) → 1 (true)

118.9

 ○–○–○ 

\(118^2=13924~~\) en \(~~139-fibonacci(2*4)=118\)
\(118^3=1643032~~\) en \(~~?=118\)
\(118^4=193877776~~\) en \(~~?=118\)
\(118^5=22877577568~~\) en \(~~?=118\)
\(118^6=2699554153024~~\) en \(~~?=118\)
\(118^7=318547390056832~~\) en \(~~?=118\)
\(118^8=37588592026706176~~\) en \(~~?=118\)
\(118^9=4435453859151328768~~\) en \(~~?=118\)
118.10

Som Der Cijfers (\(sdc\)) van \(k^{\large{118}}\) is gelijk aan het grondtal \(k\). De triviale oplossingen \(0\) en \(1\) negerend vinden we :

\(\qquad\qquad~sdc\left(1674^{\large{118}}\right)=1674\qquad\qquad~sdc\left(1764^{\large{118}}\right)=1764\)

118.11

Als expressie met enkelcijferige toepassing, resp. van \(1\) tot \(9~~\) (met dank aan Inder. J. Taneja).
\(\qquad\qquad118=11^{(1+1)}-1-1-1\)
\(\qquad\qquad118=2*2*(22+2)+22\)
\(\qquad\qquad118=3+3+(333+3)/3\)
\(\qquad\qquad118=4+4+(444-4)/4\)
\(\qquad\qquad118=5+(555+5+5)/5\)
\(\qquad\qquad118=6+(666+6)/6\)
\(\qquad\qquad118=7+777/7\)
\(\qquad\qquad118=8+(888-8)/8\)
\(\qquad\qquad118=99+9+9+9/9\)

118.12

Met de cijfers van \(1\) tot \(9\) in stijgende en dalende volgorde (met dank aan Inder. J. Taneja) :
\(\qquad\qquad118=1+23+4+5+6+7+8*9\)
\(\qquad\qquad118=9+87+6+5+4+3*2+1\)

118.13

Som der reciproken van partitiegetallen van \(118\) is \(1\) op \(341\) (driehonderdeenenveertig) wijzen.

Veertien partities hebben unieke termen.

\(~~~~(1)~~\bbox[navajowhite,3px,border:1px solid]{118=2+3+14+24+35+40}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{3}}+{\Large\frac{1}{14}}+{\Large\frac{1}{24}}+{\Large\frac{1}{35}}+{\Large\frac{1}{40}}\)

\(~~~~(2)~~\bbox[navajowhite,3px,border:1px solid]{118=2+3+15+21+35+42}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{3}}+{\Large\frac{1}{15}}+{\Large\frac{1}{21}}+{\Large\frac{1}{35}}+{\Large\frac{1}{42}}\)

\(~~~~(3)~~\bbox[navajowhite,3px,border:1px solid]{118=2+3+16+21+28+48}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{3}}+{\Large\frac{1}{16}}+{\Large\frac{1}{21}}+{\Large\frac{1}{28}}+{\Large\frac{1}{48}}\)

\(~~~~(4)~~\bbox[navajowhite,3px,border:1px solid]{118=2+5+6+14+21+70}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{5}}+{\Large\frac{1}{6}}+{\Large\frac{1}{14}}+{\Large\frac{1}{21}}+{\Large\frac{1}{70}}\)

\(~~(15)~~\bbox[navajowhite,3px,border:1px solid]{118=2+5+8+14+24+30+35}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{5}}+{\Large\frac{1}{8}}+{\Large\frac{1}{14}}+{\Large\frac{1}{24}}+{\Large\frac{1}{30}}+{\Large\frac{1}{35}}\)

\(~~(18)~~\bbox[navajowhite,3px,border:1px solid]{118=2+5+9+16+18+20+48}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{5}}+{\Large\frac{1}{9}}+{\Large\frac{1}{16}}+{\Large\frac{1}{18}}+{\Large\frac{1}{20}}+{\Large\frac{1}{48}}\)

\(~~(24)~~\bbox[navajowhite,3px,border:1px solid]{118=2+6+7+12+21+28+42}~~\) en \(~~1={\Large\frac{1}{2}}+{\Large\frac{1}{6}}+{\Large\frac{1}{7}}+{\Large\frac{1}{12}}+{\Large\frac{1}{21}}+{\Large\frac{1}{28}}+{\Large\frac{1}{42}}\)

\(~~(34)~~\bbox[navajowhite,3px,border:1px solid]{118=3+4+5+10+15+36+45}~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{5}}+{\Large\frac{1}{10}}+{\Large\frac{1}{15}}+{\Large\frac{1}{36}}+{\Large\frac{1}{45}}\)

\(~~(68)~~\bbox[navajowhite,3px,border:1px solid]{118=3+4+7+12+14+20+28+30}~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{7}}+{\Large\frac{1}{12}}+{\Large\frac{1}{14}}+{\Large\frac{1}{20}}+{\Large\frac{1}{28}}+{\Large\frac{1}{30}}\)

\(~~(70)~~\bbox[navajowhite,3px,border:1px solid]{118=3+4+8+10+14+20+24+35}~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{8}}+{\Large\frac{1}{10}}+{\Large\frac{1}{14}}+{\Large\frac{1}{20}}+{\Large\frac{1}{24}}+{\Large\frac{1}{35}}\)

\(~~(71)~~\bbox[navajowhite,3px,border:1px solid]{118=3+4+8+10+15+18+24+36}~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{8}}+{\Large\frac{1}{10}}+{\Large\frac{1}{15}}+{\Large\frac{1}{18}}+{\Large\frac{1}{24}}+{\Large\frac{1}{36}}\)

\(~~(81)~~\bbox[navajowhite,3px,border:1px solid]{118=3+4+8+10+15+18+24+36}~~\) en \(~~1={\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{8}}+{\Large\frac{1}{10}}+{\Large\frac{1}{15}}+{\Large\frac{1}{18}}+{\Large\frac{1}{24}}+{\Large\frac{1}{36}}\)

\((116)~~\bbox[navajowhite,3px,border:1px solid]{118=4+5+6+7+9+14+28+45}~~\) en \(~~1={\Large\frac{1}{4}}+{\Large\frac{1}{5}}+{\Large\frac{1}{6}}+{\Large\frac{1}{7}}+{\Large\frac{1}{9}}+{\Large\frac{1}{14}}+{\Large\frac{1}{28}}+{\Large\frac{1}{45}}\)

\((195)~~\bbox[navajowhite,3px,border:1px solid]{118=4+6+7+8+9+14+18+24+28}~~\) en \(~~1={\Large\frac{1}{4}}+{\Large\frac{1}{6}}+{\Large\frac{1}{7}}+{\Large\frac{1}{8}}+{\Large\frac{1}{9}}+{\Large\frac{1}{14}}+{\Large\frac{1}{18}}+{\Large\frac{1}{24}}+{\Large\frac{1}{28}}\)

(OEIS A125726)

118.14
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
“Allemaal Getallen”

\(\Huge\bbox[border:0]{⏮}\)

\(\Huge\bbox[border:0]{⯬}\)

\(\Huge\bbox[border:0]{⏴}\)

\(\Huge\bbox[border:0]{⏵}\)

\(\Huge\bbox[border:0]{⯮}\)

\(\Huge\bbox[border:0]{⏭}\)

\(118\)\(2*59\)\(4\)\(180\)
\(1,2,59,118\)
\(1110110_2\)\(166_8\)\(76_{16}\)
   

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 20 maart 2025