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40 (szám)

Ez a szócikk a negyvenes számról szól. A 40. évről szóló cikket lásd itt: 40.
40
(negyven)
… 36 37 38 39 « 40 » 41 42 43 44 …
… 0 10 20 30 • 50 60 70 80 …
… 0 • 100 200 300 400 …
Tulajdonságok
Normálalak4 · 101
Kanonikus alak23 · 51
Osztók1, 2, 4, 5, 8, 10, 20, 40
Római számmalXL
Számrendszerek
Bináris alak1010002
Oktális alak508
Hexadecimális alak2816
Számelméleti függvények értékei
Euler-függvény16
Möbius-függvény0
Mertens-függvény0
Osztók száma8
Osztók összege90
bővelkedő szám
Valódiosztó-összeg49

A 40 (negyven) a 39 és 41 között található természetes szám.

A szám a matematikában

A tízes számrendszerbeli 40-es a kettes számrendszerben 101000, a nyolcas számrendszerben 50, a tizenhatos számrendszerben 28 alakban írható fel.

A 40 páros szám, összetett szám, azon belül félprím, kanonikus alakban a 23 · 51 szorzattal, normálalakban a 4 · 101 szorzattal írható fel. Nyolc osztója van a természetes számok halmazán, ezek növekvő sorrendben: 1, 2, 4, 5, 8, 10, 20 és 40.

A negyven nyolcszögszám, ötszögalapú piramisszám.[1] Osztóinak egy részét összeadva megkapjuk a 40-et, ezért áltökéletes szám.

40 a legkisebb n, amire pontosan 9 megoldása van a φ(x) = n egyenletnek.

A 40 a megoldása a n-királynő problémának n = 7-re.

A 40 5-sima szám, más néven szabályos szám.

A 40 repdigit 3-as számrendszerben és Harshad-szám tízesben.

Három szám valódiosztó-összegeként áll elő, ezek a 44, a 74 és a 81..[2][3]

A tudományban

A Bibliában

A 40-es szám többször is szerepel a Bibliában.

  • jelölheti egy-egy nemzedék éveinek számát: negyvenéves vándorlás a pusztában
  • Negyvenéves nyugalom Izraelben az egyes bírák által végrehajtott felszabadítások után
  • A vízözön negyven nap és negyven éjjel (1Móz. 7,12).
  • Mózes negyvennapos tartózkodása a Sínai-hegyen és böjtje (5Móz. 8,11), (5Móz. 9,18), (5Móz. 10,10).
  • Illés negyvennapos vándorlása és böjtje a Hóreb hegyéig (1Kir.19,8).
  • Krisztus negyvennapos böjtje a pusztában (Máté 4,2).[4]

Az irodalomban

Egyéb

Jegyzetek

Commons:Category:40 (number)
A Wikimédia Commons tartalmaz 40 (szám) témájú médiaállományokat.

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