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- Untouchable_number abstract "An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself).For example, the number 4 is not untouchable as it is equal to the sum of the proper divisors of 9: 1 + 3 = 4. The number 5 is untouchable as it is not the sum of the proper divisors of any positive integer: 5 = 1 + 4 is the only way to write 5 as the sum of distinct positive integers including 1, but if 4 divides a number, 2 does also, so 1 + 4 cannot be the sum of all of any number's proper divisors (since the list of factors would have to contain both 4 and 2).The first few untouchable numbers are:2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210, 216, 238, 246, 248, 262, 268, 276, 288, 290, … (sequence A005114 in OEIS)The number 5 is believed to be the only odd untouchable number, but this has not been proven: it would follow from a slightly stronger version of the Goldbach conjecture. Thus it appears that besides 2 and 5, all untouchable numbers are composite numbers. No perfect number is untouchable, since, at the very least, it can be expressed as the sum of its own proper divisors.There are infinitely many untouchable numbers, a fact that was proven by Paul Erdős.No untouchable number is one more than a prime number, since if p is prime, then the sum of the proper divisors of p2 is p + 1. Also, no untouchable number is three more than a prime number, except 5, since if p is an odd prime then the sum of the proper divisors of 2p is p + 3.".
- Untouchable_number wikiPageID "882410".
- Untouchable_number wikiPageRevisionID "596043907".
- Untouchable_number hasPhotoCollection Untouchable_number.
- Untouchable_number name "Least m such that sum of aliquot parts of m equals n or 0 if no such number exists".
- Untouchable_number sequencenumber "A070015".
- Untouchable_number subject Category:Divisor_function.
- Untouchable_number subject Category:Integer_sequences.
- Untouchable_number type Abstraction100002137.
- Untouchable_number type Arrangement107938773.
- Untouchable_number type Group100031264.
- Untouchable_number type IntegerSequences.
- Untouchable_number type Ordering108456993.
- Untouchable_number type Sequence108459252.
- Untouchable_number type Series108457976.
- Untouchable_number comment "An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself).For example, the number 4 is not untouchable as it is equal to the sum of the proper divisors of 9: 1 + 3 = 4.".
- Untouchable_number label "Nombre intouchable".
- Untouchable_number label "Numero intoccabile".
- Untouchable_number label "Onaanraakbaar getal".
- Untouchable_number label "Untouchable number".
- Untouchable_number label "Неприкосновенное число".
- Untouchable_number label "不可及数".
- Untouchable_number sameAs Nombre_intouchable.
- Untouchable_number sameAs Numero_intoccabile.
- Untouchable_number sameAs 불가촉_수.
- Untouchable_number sameAs Onaanraakbaar_getal.
- Untouchable_number sameAs m.03lgjp.
- Untouchable_number sameAs Q1193504.
- Untouchable_number sameAs Q1193504.
- Untouchable_number sameAs Untouchable_number.
- Untouchable_number wasDerivedFrom Untouchable_number?oldid=596043907.
- Untouchable_number isPrimaryTopicOf Untouchable_number.