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- Friendly_number abstract "In number theory, friendly numbers are two or more natural numbers with a common abundancy, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same abundancy form a friendly pair; n numbers with the same abundancy form a friendly n-tuple.Being mutually friendly is an equivalence relation, and thus induces a partition of the positive naturals into clubs (equivalence classes) of mutually friendly numbers.A number that is not part of any friendly pair is called solitary.The abundancy of n is the rational number σ(n) / n, in which σ denotes the sum of divisors function. A number n is a friendly number if there exists m ≠ n such that σ(m) / m = σ(n) / n. Note that abundancy is not the same as abundance which is defined as σ(n) − 2n.Abundancy may also be expressed as where denotes a divisor function with equal to the sum of the k-th powers of the divisors of n.The numbers 1 through 5 are all solitary. The smallest friendly number is 6, forming for example the friendly pair (6, 28) with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases. There are several unsolved problems related to the friendly numbers.In spite of the similarity in name, there is no specific relationship between the friendly numbers and the amicable numbers or the sociable numbers, although the definitions of the latter two also involve the divisor function.".
- Friendly_number wikiPageID "3821872".
- Friendly_number wikiPageRevisionID "594868907".
- Friendly_number hasPhotoCollection Friendly_number.
- Friendly_number title "Abundancy".
- Friendly_number title "Friendly Number".
- Friendly_number title "Friendly Pair".
- Friendly_number title "Solitary Number".
- Friendly_number urlname "Abundancy".
- Friendly_number urlname "FriendlyNumber".
- Friendly_number urlname "FriendlyPair".
- Friendly_number urlname "SolitaryNumber".
- Friendly_number subject Category:Divisor_function.
- Friendly_number subject Category:Integer_sequences.
- Friendly_number subject Category:Number_theory.
- Friendly_number subject Category:Unsolved_problems_in_mathematics.
- Friendly_number type Abstraction100002137.
- Friendly_number type Arrangement107938773.
- Friendly_number type Attribute100024264.
- Friendly_number type Condition113920835.
- Friendly_number type Difficulty114408086.
- Friendly_number type Group100031264.
- Friendly_number type IntegerSequences.
- Friendly_number type Ordering108456993.
- Friendly_number type Problem114410605.
- Friendly_number type Sequence108459252.
- Friendly_number type Series108457976.
- Friendly_number type State100024720.
- Friendly_number type UnsolvedProblemsInMathematics.
- Friendly_number comment "In number theory, friendly numbers are two or more natural numbers with a common abundancy, the ratio between the sum of divisors of a number and the number itself.".
- Friendly_number label "Friendly number".
- Friendly_number label "友誼數".
- Friendly_number sameAs m.02p7qns.
- Friendly_number sameAs Q1707307.
- Friendly_number sameAs Q1707307.
- Friendly_number sameAs Friendly_number.
- Friendly_number wasDerivedFrom Friendly_number?oldid=594868907.
- Friendly_number isPrimaryTopicOf Friendly_number.