Univalence axiom

In mathematics, a Descartes number is a number which is close to being a perfect number. They are named for René Descartes who observed that the number D = 3²⋅7²⋅11²⋅13²⋅22021 = 198585576189 would be an odd perfect number if only 22021 were a prime number, since the sum-of-divisors function for D satisfies

$\sigma (D)=(3^{2}+3+1)\cdot (7^{2}+7+1)\cdot (11^{2}+11+1)\cdot (13^{3}+13+1)\cdot (22021+1)\ .$

A Descartes number is defined as an odd number n = m⋅p where m and p are coprime and 2n = σ(m)⋅(p+1). The example given is the only one currently known.

If m is an odd almost perfect number, that is, σ(m) = 2m−1, then m(2m−1) is a Descartes number.

References

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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534