Superperfect Number
In mathematics a superperfect number is a positive integer n that satisfies
where σ is the divisor function. Superperfect numbers are a generalization of perfect numbers. The term was coined by Suryanarayana (1969).
The first few superperfect numbers are
- 2, 4, 16, 64, 4096, 65536, 262144 (sequence A019279 in OEIS).
If n is an even superperfect number then n must be a power of 2, 2k, such that 2k+1-1 is a Mersenne prime.
It is not known whether there are any odd superperfect numbers. An odd superperfect number n would have to be a square number such that either n or σ(n) is divisible by at least three distinct primes. There are no odd superperfect numbers below 7x1024.
Read more about Superperfect Number: Generalisations
Famous quotes containing the word number:
“Even in ordinary speech we call a person unreasonable whose outlook is narrow, who is conscious of one thing only at a time, and who is consequently the prey of his own caprice, whilst we describe a person as reasonable whose outlook is comprehensive, who is capable of looking at more than one side of a question and of grasping a number of details as parts of a whole.”
—G. Dawes Hicks (1862–1941)