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- Multiply_perfect_number abstract "In mathematics, a multiply 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 called k-perfect (or k-fold perfect) if and only if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and only if it is 2-perfect. A number that is k-perfect for a certain k is called a multiply perfect number. As of 2014, k-perfect numbers are known for each value of k up to 11.It can be proven that: For a given prime number p, if n is p-perfect and p does not divide n, then pn is (p+1)-perfect. This implies that an integer n is a 3-perfect number divisible by 2 but not by 4, if and only if n/2 is an odd perfect number, of which none are known. If 3n is 4k-perfect and 3 does not divide n, then n is 3k-perfect.↑".
- Multiply_perfect_number wikiPageExternalLink 275.
- Multiply_perfect_number wikiPageExternalLink page.php?sort=MultiplyPerfect.
- Multiply_perfect_number wikiPageExternalLink mpn.html.
- Multiply_perfect_number wikiPageID "321801".
- Multiply_perfect_number wikiPageRevisionID "606066093".
- Multiply_perfect_number hasPhotoCollection Multiply_perfect_number.
- Multiply_perfect_number subject Category:Integer_sequences.
- Multiply_perfect_number type Abstraction100002137.
- Multiply_perfect_number type Arrangement107938773.
- Multiply_perfect_number type Group100031264.
- Multiply_perfect_number type IntegerSequences.
- Multiply_perfect_number type Ordering108456993.
- Multiply_perfect_number type Sequence108459252.
- Multiply_perfect_number type Series108457976.
- Multiply_perfect_number comment "In mathematics, a multiply 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 called k-perfect (or k-fold perfect) if and only if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and only if it is 2-perfect. A number that is k-perfect for a certain k is called a multiply perfect number.".
- Multiply_perfect_number label "Multiply perfect number".
- Multiply_perfect_number label "Nombre parfait multiple".
- Multiply_perfect_number label "Numero moltiplicativamente perfetto".
- Multiply_perfect_number label "倍積完全数".
- Multiply_perfect_number label "多重完全數".
- Multiply_perfect_number sameAs Nombre_parfait_multiple.
- Multiply_perfect_number sameAs Numero_moltiplicativamente_perfetto.
- Multiply_perfect_number sameAs 倍積完全数.
- Multiply_perfect_number sameAs m.01vlym.
- Multiply_perfect_number sameAs Q1755843.
- Multiply_perfect_number sameAs Q1755843.
- Multiply_perfect_number sameAs Multiply_perfect_number.
- Multiply_perfect_number wasDerivedFrom Multiply_perfect_number?oldid=606066093.
- Multiply_perfect_number isPrimaryTopicOf Multiply_perfect_number.