^Weisstein, Eric W. "Primitive Abundant Number". MathWorld.
^Erdős adopts a wider definition that requires a primitive abundant number to be not deficient, but not necessarily abundant (Erdős, Surányi and Guiduli. Topics in the Theory of Numbers p214. Springer 2003.). The Erdős definition allows perfect numbers to be primitive abundant numbers too.
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a primitiveabundantnumber is an abundantnumber whose proper divisors are all deficient numbers. For example, 20 is a primitiveabundantnumber because:...
quasiperfect number, although none have yet been found. Every abundantnumber is a multiple of either a perfect number or a primitiveabundantnumber. Numbers...
In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including...
semiperfect number is 945 (see, e.g., Friedman 1993). A semiperfect number is necessarily either perfect or abundant. An abundantnumber that is not semiperfect...
In number theory, a highly abundantnumber is a natural number with the property that the sum of its divisors (including itself) is greater than the sum...
In number theory, a colossally abundantnumber (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors...
perfect number. Most abundant numbers are also semiperfect; abundant numbers which are not semiperfect are called weird numbers. Hyperperfect number Leinster...
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...
integer m a primitiveabundantnumber is an abundantnumber whose proper divisors are all deficient numbers a weird number is an abundantnumber that is not...
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is...
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci...
with σ(n) = 2n, and abundant numbers with σ(n) > 2n. Nicomachus was the first to subdivide numbers into deficient, perfect, or abundant, in his Introduction...
the number, whereas an abundantnumber has a sum of its proper divisors that is larger than the number itself. Primitiveabundant numbers are abundant numbers...
is the number of numbers in this cycle. If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example...
every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form...
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy...
perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is...
enumerations, are studied in combinatorics. The most primitive method of representing a natural number is to use one's fingers, as in finger counting. Putting...
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and...
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