Sublime number

Sublime number

In mathematics, a sublime number is a positive integer which has a perfect number of positive divisors (including itself), and whose positive divisors add up to another perfect number. [MathPages article, [http://www.mathpages.com/home/kmath202/kmath202.htm "Sublime Numbers"] .]

The number 12, for example, is a sublime number. It has a perfect number of positive divisors (6): 1, 2, 3, 4, 6, and 12, and the sum of these is again a perfect number: 1 + 2 + 3 + 4 + 6 + 12 = 28.

There are only two known sublime numbers, 12 and (2126)(261 − 1)(231 − 1)(219 − 1)(27 − 1)(25 − 1)(23 − 1) OEIS|id=A081357. [Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning" New York: Oxford University Press (2003): 215] The second of these has 76 decimal digits::6086555670238378 989670371734243169622657830773 351885970528324860512791691264.

References


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Sublime (band) — Infobox musical artist Name = Sublime Img capt = Img size = Background = group or band Origin = Long Beach, California, U.S. Genre = Ska punk Third wave ska Reggae Years active = 1988–1996 Label = MCA, Skunk Associated acts = Long Beach Dub… …   Wikipedia

  • Sublime (comics) — Superherobox| caption=John Sublime with Martha Johansson in New X Men #119. Art by Igor Kordey character name=Sublime real name= species=Sentient bacteria publisher=Marvel Comics debut= New X Men Annual 2001 creators=Grant Morrison (writer),… …   Wikipedia

  • Sublime (groupe) — Pour les articles homonymes, voir sublime (homonymie). Sublime était un groupe américain de Long Beach, en Californie. Il fut actif de 1988 à 1996. Le mélange subtil des genres (tels que le reggae, ska, hip hop, dub, et punk rock), l humour et le …   Wikipédia en Français

  • number game — Introduction       any of various puzzles and games that involve aspects of mathematics.       Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved.… …   Universalium

  • Number one modern rock hits of 1996 — These are the Billboard magazine Modern Rock Tracks number one hits of 1996. Issue date Song Artist Reference(s) January 6 Wonderwall Oasis [1] January 13 [2] January 20 …   Wikipedia

  • Prime number — Prime redirects here. For other uses, see Prime (disambiguation). A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is… …   Wikipedia

  • Perfect number — In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect… …   Wikipedia

  • Highly composite number — This article is about numbers having many divisors. For numbers factorized only to powers of 2, 3, 5 and 7 (also named 7 smooth numbers), see Smooth number. A highly composite number (HCN) is a positive integer with more divisors than any… …   Wikipedia

  • Composite number — A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number. So, if n > 0 is an integer and… …   Wikipedia

  • 12 (number) — ← 11 13 → 12 ← 10 11 12 13 14 15 16 …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”