Do all aliquot sequences eventually end with a prime number, a perfect number, or a set of amicable or sociable numbers? (Catalan's aliquot sequence conjecture)
(more unsolved problems in mathematics)
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
all aliquotsequences eventually end with a prime number, a perfect number, or a set of amicable or sociable numbers? (Catalan's aliquotsequence conjecture)...
numbers, abundant numbers, and untouchable numbers, and to define the aliquotsequence of a number. For example, the proper divisors of 12 (that is, the positive...
the aliquot parts of an integer Aliquotsequence, a sequence of integers in which each number is the aliquot sum of the previous number Aliquot stringing...
In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence. They are generalizations of the concepts of perfect numbers...
other words a number which forms an aliquotsequence of period 1. Numbers that are members of an aliquotsequence with period greater than 2 are known...
is different from n {\displaystyle n} is called a proper divisor or an aliquot part of n . {\displaystyle n.} A number that does not evenly divide n {\displaystyle...
Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known...
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