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...own as <math>\mathcal{S}</math>-perfect numbers, are an extension of the [[perfect number]]s. ...nslator-first = J. M. |translator-last=de Koninck |title=Those Fascinating Numbers |url=https://archive.org/details/thosefascinating0000koni/page/40/mode/2up ...

...hematical constant created by concatenating the decimal representations of perfect squares<ref>Square number</ref> in sequential order. This results in an inf The Squared Constant is formed by writing each perfect square consecutively after a decimal point: ...

{{Short description|Abundant number whose proper divisors are all deficient numbers}} .... The Erdős definition allows [[perfect number]]s to be primitive abundant numbers too.</ref> ...

| OEIS_name = Erdős-Nicolas numbers ...]], an '''Erdős–Nicolas number''' is a number that is not [[perfect number|perfect]], but that equals one of the [[partial sum]]s of its [[divisor]]s. ...

...t=Elena|last=Deza|author-link=Elena Deza|title=Mersenne Numbers And Fermat Numbers|page=263|publisher=World Scientific|year=2021|isbn=978-9811230332}}</ref> ...name=oeis>{{cite OEIS|A052294|mode=cs2}}</ref> The sequence of pernicious numbers begins ...

{{Short description|In mathematics, a group-theoretic analogue of the perfect numbers}} ...ritten in 1996 but not published until 2001.{{r|leinster}} He called them "perfect groups"{{r|leinster}} and later "immaculate groups",{{r|brunault}} ...

In [[commutative algebra|commutative]] algebra, a '''perfect ideal''' is a proper [[ideal (ring theory)|ideal]] <math>I</math> in a [[No A perfect ideal is [[Unmixed ideal|unmixed]]. ...

{{short description|Characterization of even perfect numbers}} ...perfect numbers and Mersenne primes|the theorem on the infinitude of prime numbers|Euclid's theorem}} ...

{{Short description|Number which would have been an odd perfect number if one of its composite factors were prime}} ...2</sup>&thinsp;⋅&thinsp;(22⋅1001 − 1) {{=}} 198585576189}} would be an odd perfect number if only {{math|22021}} were a [[prime number]], since the [[sum-of-d ...

In [[number theory]], a '''perfect digit-to-digit invariant''' ('''PDDI'''; also known as a '''Munchausen numb | title = The Penguin Dictionary of Curious and Interesting Numbers ...

...er is a sociable Meertens number with <math>k = 1</math>, and a [[Amicable numbers|amicable]] '''Meertens number''' is a sociable Meertens number with <math>k == Meertens numbers and cycles of ''F_b'' for specific ''b'' == ...

...elated to [[Dilworth's theorem]] on the widths of partial orders, to the [[perfect graph|perfection]] of [[comparability graph]]s, to the [[Gallai–Hasse–Roy–V ...f these sets, every pair of numbers forms a ratio less than two, so no two numbers within one of these sets can be divisible. ...

...thematics of [[figurate number]]s, the '''cannonball problem''' asks which numbers are both [[Square number|square]] and [[square pyramidal number|square pyra ...ite OEIS|sequencenumber=A000292|name=Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6}}</ref> ...

...due field of a valuation|residue field]] <math>k</math> is [[perfect field|perfect]] of [[characteristic (algebra)|characteristic]] <math>p</math>, there is a ...n | last1=Koblitz | first1=Neal | author1-link=Neal Koblitz | title=p-adic Numbers, p-adic Analysis, and Zeta-Functions | publisher=[[Springer-Verlag]] | loca ...

...or example, in [[graph theory]] to obtain upper bounds for the number of [[perfect matching]]s in a [[bipartite graph]]. ...nent is therefore bounded by the product of the [[geometric mean]]s of the numbers from <math>1</math> to <math>r_i</math> for <math>i=1, \ldots , n</math>. E ...

...irst1=Yan|last2=Liu|first2=Guizhen|date=2002|title=The fractional matching numbers of graphs|journal=Networks|language=en|volume=40|issue=4|pages=228–231|doi= == Perfect fractional matching == ...

As a special case of this, a '''<math>(p,q)</math>-shuffle''', for numbers <math>p</math> and <math>q</math> with <math>p+q=n</math>, is a riffle in w ==Perfect shuffles== ...

...p://www.cs.umd.edu/Honors/reports/NarcissisticNums/NarcissisticNums.html ''Perfect and PluPerfect Digital Invariants''] {{webarchive|url=https://web.archive.o Let <math>n</math> be a [[natural number]]. The '''perfect digital invariant function''' (also known as a '''happy function''', from [ ...

...ssue = 4 }}. See line 19 of table, p. 411, completely characterizing which numbers of hexagons are possible in a fullerene.</ref> ...ne from which one can remove four edges to obtain a subgraph with a unique perfect matching.<ref>{{citation ...

...hat is, it is generally the sum of [[unit fraction]]s. If infinitely many numbers have their reciprocals summed, generally the terms are given in a certain s If only finitely many numbers are included, the key issue is usually to find a simple expression for the ...