Thus, an integer $n\geq1$ is a perfect number if
For example, the numbers 6, 28, 496, 8128, 33550336$,\ldots,$ are perfect.
3 KB (430 words) - 19:37, 21 March 2024
...l almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least 6 prime factors.
If $m$ is an odd almost perfect number then $m(2m-1)$ is a [[Descartes number]].
2 KB (260 words) - 19:44, 17 November 2023
...}.P$: it is not known if there are any odd perfect numbers. An ''[[almost perfect number]]'' $n$ similarly has the property that $\sigma(n) = 2n-1$: these in
* Kishore, Masao. "On odd perfect, quasiperfect, and odd almost perfect numbers". Mathematics of Computation '''36''' (1981) 583–586. {{ZBL|0472.10007}}
2 KB (268 words) - 19:41, 17 November 2023
...f divisors]]: these are also called ''Øre numbers''. The first seven such numbers are
An even [[perfect number]] is a harmonic number.
2 KB (222 words) - 14:19, 12 November 2023
A divisor $d$ of a natural number $n$ such that $d$ and $n/d$ are [[coprime numbers]], having no common factor other than 1. Equivalently, $d$ is a unitary di
...It is not known whether or not there are infinitely many unitary perfect numbers, or indeed whether there are any further examples beyond the five already k
2 KB (317 words) - 19:43, 17 November 2023
...perfect rings are defined similarly. A left perfect ring need not be right perfect.
The following properties of a ring $R$ are equivalent: 1) $R$ is a left perfect ring; 2) every set of pairwise orthogonal idempotents of $R$ is finite, and
3 KB (491 words) - 19:59, 30 October 2016
A number which is close to being a [[perfect number]]. They are named for René Descartes who observed that the number
would be an odd perfect number if only 22021 were a [[prime number]], since the [[Sum of divisors|s
1 KB (164 words) - 07:50, 4 November 2023
...d $b$ are rational numbers, $b\ne 0$, and $d$ is an integer which is not a perfect square. A real number $\alpha$ is a quadratic irrationality if and only if
683 bytes (103 words) - 20:31, 1 October 2016
...ervals (adjacent intervals), the total of whose length is 1, is the Cantor perfect set (Cantor set; Cantor ternary set; Cantor discontinuum).
...hough the standard Cantor set has measure zero, there exists nowhere-dense perfect compacta on the unit interval with measure arbitrarily close to 1.
4 KB (527 words) - 09:11, 26 March 2023
$#C+1 = 137 : ~/encyclopedia/old_files/data/P072/P.0702070 Perfect measure
...ions that occur in general measure theory do not arise if one restricts to perfect measures.
8 KB (1,244 words) - 08:05, 6 June 2020
...is problem is closely related with the problem on the existence of perfect numbers.
The Lucas test provides a very simple method to establish primality of these numbers. This test consists of the following (cf. [[#References|[a2]]]). Define $S_
2 KB (344 words) - 06:44, 22 March 2024
set. There exists perfect sets (cf. [[Perfect set|Perfect set]]) of measure zero that are $ M $-
is an integer, that is, whether a set of numbers is a $ U $-
6 KB (865 words) - 22:26, 29 January 2020
...rly, these numbers are in fact perfect or abundant (i.e. "non-deficient") numbers.
...$b = 5$, $c = 7$, $abcd$ is abundant for any prime number $d > c$. Of the numbers $\leq 1000$, $52$ are abundant.
15 KB (2,194 words) - 05:54, 15 February 2024
...ect ring]]) there is a proper class of p-test modules. If $R$ is not right perfect, then it is consistent with ZFC (cf. [[Set theory|Set theory]]; [[Zermelo a
...entified in [[#References|[a3]]]. If $R$ is right hereditary but not right perfect, then it is consistent with ZFC that there is a proper class of p-test modu
5 KB (732 words) - 17:46, 1 July 2020
A code intended for the control of the functioning of an adder. When adding numbers represented in the binary number system, a single slip in the functioning o
described around any two numbers of a code do not intersect (that is, if the minimum distance of the code is
8 KB (1,189 words) - 09:46, 26 March 2023
image of the set of irrational numbers, an ${\mathcal A}$-set can be defined as a
continuous image of the set of irrational numbers. A countable
2 KB (327 words) - 14:21, 15 August 2023
The sequence of natural numbers $a_1,a_2,\dots$ defined by the rule $a_1 = n$, $a_{k+1} = s(a_k)$ where $s(
...ers]]): aliquot cycles of length greater than 2 are also termed ''sociable numbers''.
2 KB (331 words) - 14:02, 12 November 2023
...ots,X_n\}\}$ are generally called quasi-analytic $k$-algebras. If $k$ is a perfect field, an analytic ring is an [[Excellent ring|excellent ring]].
2 KB (341 words) - 12:10, 25 August 2014
and is such that any perfect irreducible inverse image of the space $ X $
...connected by a single-valued or multi-valued [[Perfect irreducible mapping|perfect irreducible mapping]] $ f: X \rightarrow Y $,
10 KB (1,505 words) - 04:04, 9 May 2022
...mapping|Closed mapping]]; [[Open mapping|Open mapping]]; [[
Perfect mapping|
Perfect mapping]]; [[Quotient mapping|Quotient mapping]]). If <img align="absmiddle
...png" />-dimensional cube. 2) A pointwise-countable base is preserved under
perfect (even under bifactorial) mappings. 3) Every closed mapping <img align="absm
15 KB (2,197 words) - 17:15, 7 February 2011