A **superabundant number** is a positive integer \( n \) for which the ratio of the sum of its divisors \( \sigma(n) \) to \( n \) is greater than the ratio for any smaller positive integer \( m \).

A Super-Poulet number is a special type of number that is defined in terms of prime numbers. Specifically, a Super-Poulet number is a natural number \( n \) such that \( n \) is a power of a prime \( p^k \) where \( k \geq 1 \) (i.e.

A **sum-free sequence** is a sequence of integers such that no two elements in the sequence sum to another element in the same sequence. In other words, if \( a \) and \( b \) are elements of the sequence, then \( a + b \) should not be an element of the sequence.

A Sublime number is a specific type of number in number theory that is defined as a natural number \( n \) for which the sum of its proper divisors (the divisors of \( n \) excluding \( n \) itself) is equal to \( n \) times the number of proper divisors of \( n \).

A Størmer number is a specific type of number in number theory that is associated with the properties of the prime factorization of positive integers. It is defined by the following property: A positive integer \( n \) is called a Størmer number if it is equal to the sum of the digits in its prime factorization, each counted with multiplicity.

A strobogrammatic number is a number that appears the same when rotated 180 degrees (or flipped upside down). This means that the individual digits in the number can be transformed into other digits (or themselves) when turned.

Stirling numbers are a part of combinatorial mathematics and come in two main types: the Stirling numbers of the first kind and the Stirling numbers of the second kind. 1. **Stirling Numbers of the First Kind**: Denoted by \( c(n, k) \), these numbers count the number of permutations of \( n \) elements with exactly \( k \) disjoint cycles.

The Stanley sequence is a mathematical sequence related to combinatorics and specific types of partitions. It was introduced by Richard P. Stanley, a prominent combinatorialist, in his research on enumerative combinatorics, particularly in the context of partitions of integers.

A **square-free integer** is an integer that is not divisible by the square of any prime number. In other words, a square-free integer cannot have any prime factor raised to a power greater than one in its prime factorization. For example: - The integer 30 is square-free because its prime factorization is \(2^1 \times 3^1 \times 5^1\); none of the prime factors are squared or higher.

The Spt function is often associated with statistical processing and time-series analysis, but the term could refer to several different contexts depending on the field. Here are a couple of possible interpretations: 1. **Spt as a Mathematical Function**: In mathematics or statistics, "Spt" could stand for a "support" function, which describes the set of points in a given space where a function is defined or has specific values.

A sphenic number is a positive integer that is the product of three distinct prime numbers. In other words, a sphenic number can be expressed in the form \( p_1 \times p_2 \times p_3 \), where \( p_1 \), \( p_2 \), and \( p_3 \) are prime numbers and \( p_1 \), \( p_2 \), and \( p_3 \) are all different from one another.

A sparsely totient number is a positive integer \( n \) for which the ratio of the Euler's totient function \( \varphi(n) \) to \( n \) is relatively small compared to other integers. More formally, a number \( n \) is considered a sparsely totient number if: \[ \frac{\varphi(n)}{n} < \frac{1}{\log n} \] for sufficiently large \( n \).

A sorting number, although not a widely recognized term, can refer to concepts related to sorting algorithms or sorting operations in computer science and data management. Here are a few potential interpretations of the term "sorting number": 1. **Sorting Algorithm Complexity**: In the context of sorting algorithms, a sorting number could refer to the time complexity or efficiency of an algorithm used to sort a dataset, such as O(n log n) for algorithms like mergesort or quicksort.

The Somos sequence refers to a family of recursively defined sequences discovered by the mathematician Edward Somos. They are notable for their interesting properties and connections to combinatorial mathematics and number theory.

A sociable number is a number that forms a closed chain with other numbers through a specific process involving the sum of its proper divisors. More formally, a sociable number is part of a group of numbers where each number in the group is the sum of the proper divisors of the preceding number.

A **smooth number** (or **friable number**) is a positive integer that has no prime factors larger than a certain number. In mathematical terms, a number \( n \) is called \( B \)-smooth if all of its prime factors are less than or equal to \( B \).

"Singly even" and "doubly even" typically refer to types of numbers in the context of mathematics, particularly in discussing properties of integers or sets of integers. 1. **Singly Even Numbers**: A number is termed "singly even" if it is divisible by 2 but not by 4. In other words, singly even numbers can be expressed in the form \(4k + 2\), where \(k\) is an integer.

"Sequences" is a book written by American author and poet, John R. McTavish. It comprises a collection of poems that explore various themes, including nature, humanity, and the interconnectedness of life. The work delves into the experiences and emotions that shape human existence, often employing vivid imagery and reflective language.

A semiperfect number, also known as a weakly perfect number, is a type of integer that can be defined in the context of its divisors. Specifically, a positive integer \( n \) is considered semiperfect if the sum of some of its divisors (excluding the number itself) is equal to \( n \). For example, consider the number 12.

The Schröder–Hipparchus number, denoted \( \text{SH}(n) \), is a sequence of numbers that counts the different ways to draw non-crossing partitions of a set with \( n \) elements. Specifically, these numbers are related to various combinatorial structures, including certain types of trees and the enumeration of non-crossing partitions.