Highly Cototient Number

In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation

x − φ(x) = k,

than any other integer below k and above one. Here, φ is Euler's totient function. There are infinitely many solutions to the equation for k = 1 so this value is excluded in the definition. The first few highly cototient numbers are:

2, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 119, 167, 209, 269, 299, 329, 389, 419, 509, 629, 659, 779, 839, 1049, 1169, 1259, 1469, 1649, 1679, 1889 (sequence A100827 in OEIS).

There are many odd highly cototient numbers. In fact, after 8, all the numbers listed above are odd, and after 167 all the numbers listed above are congruent to 9 modulo 10.

The concept is somewhat analogous to that of highly composite numbers. Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers. Computations become harder, since integer factorization does, as the numbers get larger.

Read more about Highly Cototient NumberPrimes

Other articles related to "number, highly cototient number, highly cototient numbers, highly, cototient number":

4000 (number) - Selected Numbers in The Range 4001–4999
... 4005 – triangular number 4007 – safe prime 4010 – magic constant of n×n normal magic square and n-queens problem for n = 20 ... Sophie Germain prime 4028 – sum of the first 45 primes 4030 – third weird number 4031 – sum of the cubes of the first six primes 4032 – pronic number 4033 – sixth super-Poulet ... Also record number of wickets taken in first-class cricket by Wilfred Rhodes ...
Highly Cototient Number - Primes
... The first few highly cototient numbers which are primes (sequence A105440 in OEIS) are 2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839 ... totient function Jordan's totient function Nontotient Noncototient Highly totient number Sparsely totient number Highly cototient number Prime number classes By ...

Famous quotes containing the words number and/or highly:

    As Jerome expanded, its chances for the title, “the toughest little town in the West,” increased and when it was incorporated in 1899 the citizens were able to support the claim by pointing to the number of thick stone shutters on the fronts of all saloons, gambling halls, and other places of business for protection against gunfire.
    —Administration in the State of Ariz, U.S. public relief program (1935-1943)

    a highly respectable gondolier,
    Who promised the Royal babe to rear
    And teach him the trade of a timoneer
    With his own beloved brattling.
    Sir William Schwenck Gilbert (1836–1911)