Sparsely totient number information

In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n, φ ( m ) > φ...

A highly totient number k {\displaystyle k} is an integer that has more solutions to the equation ϕ ( x ) = k {\displaystyle \phi (x)=k} , where ϕ {\displaystyle...

In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function...

function of a prime power can be expressed in terms of the Euler totient. Any number that is not 1 or a prime power can be written uniquely as the product...

6089, 6719, 9029, 9239, ... (sequence A105440 in the OEIS) Highly totient number Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)"...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...

polygonal number a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r =...

A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the...

primorial number system) have a lower proportion of repeating fractions than any smaller base. Every primorial is a sparsely totient number. The n-compositorial...

In number theory, a deficient number or defective number is a positive integer n for which the sum of divisors of n is less than 2n. Equivalently, it...

In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy...

single number 1. Some other more technical properties of prime numbers also do not hold for the number 1: for instance, the formulas for Euler's totient function...

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...

triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided...

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2...

In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A...

In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that...

A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The n-th heptagonal number is given by the formula...

the French-Belgian mathematician Eugène Charles Catalan. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients...