\(118=28+29+30+31\) (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)

\(\qquad~~~~\)(fully searched up to \(z=1000)\)

\(\qquad~~~~\)(oplossingen met vijf vijfcijfer_termen door Joe Wetherell)

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

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

\(\qquad~~~~\bbox[3px,border:1px blue solid]{953^5+1114^5+1341^5+1993^5+(-2073)^5}\)

\(\qquad~~~~\bbox[3px,border:1px blue solid]{10097^5+18101^5+(-22806)^5+(-27952)^5+29188^5}\)

\(\qquad~~~~\bbox[3px,border:1px blue solid]{19120^5+66010^5+(-68647)^5+(-70195)^5+72280^5}\)

\(\qquad~~~~\bbox[3px,border:1px blue solid]{44260^5+78438^5+78690^5+(-78907)^5+(-79103)^5}\)

118.2

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

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

118.3
\(118\) 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

\(118\) 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.

118.6

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
Het kleinste getal dat exact \(118\) delers heeft is \(864691128455135232=2^{58}*3\). (OEIS A005179) 118.15
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
“Allemaal Getallen”

⏮

⯬

⏴

⏵

⯮

⏭

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

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 13 augustus 2025