Aliquot sum information

In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself...

integer Aliquot sum, the sum of the aliquot parts of an integer Aliquot sequence, a sequence of integers in which each number is the aliquot sum of the previous...

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...

for which the sum of divisors of n is less than 2n. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than n...

14 = 28. The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently...

expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their...

or sum-of-divisors function, and the subscript is often omitted, so σ(n) is the same as σ1(n) (OEIS: A000203). The aliquot sum s(n) of n is the sum of...

2023-06-28. Sloane, N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line...

in the aliquot sequence for ten (10, 8, 7, 1, 0) that is rooted in the prime 7-aliquot tree. According to conjecture, ten is the average sum of the proper...

= m + 1, where s(n) is the aliquot sum of n: an equivalent condition is that σ(m) = σ(n) = m + n + 1, where σ denotes the sum-of-divisors function. The...

In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence. They are generalizations of the concepts of perfect numbers and...