Solved

Sum powers of e-divisors
In number theory the function produces the sum of divisors of an integer raised to the power . Setting sums the divisors, as ...

3 months ago

Solved

Count the e-divisors of an integer
Cody Problem 2664 asks us to count the divisors of an integer, and Cody Problem 60843 involves listing the e-divisors of an inte...

3 months ago

Solved

Determine the e-divisors of an integer
From MathWorld: is called an e-divisor (or exponential divisor) of a number with prime factorization if and where for...

3 months ago

Solved

List the notes of a major scale
If you have seen The Sound of Music, then you are familiar with the major scale: do, re, mi, fa, sol, la, ti, do. The C major sc...

3 months ago

Solved

Construct the number counts sequence
A sequence is constructed in the following way. The zeroth term is 1, and the next terms are determined by counting the number i...

3 months ago

Solved

List the first of three consecutive square-free numbers
The numbers 13, 14, and 15 are consecutive, of course, but they also share the property of being square-free. That is, each numb...

3 months ago

Solved

Count the primes resulting from changing one digit of a number
If you start with the number 24 and seek primes by changing a single digit, you can find two: 23 and 29. If you start with 130, ...

3 months ago

Solved

Solve an easy binary puzzle
A binary puzzle presents a square grid (or matrix) of cells in which each cell must be 0 or 1. The finished puzzle must follow t...

3 months ago

Solved

Convert integers from base 10 to proper primary notation
This problem is the companion to Cody Problem 60782. The proper primary system of expressing non-negative numbers has three digi...

3 months ago

Solved

Identify points inside a Reuleaux triangle
Write a function to identify points that lie in or on a Realeaux triangle, which is a curve of constant width. The input to the ...

3 months ago

Solved

Determine whether a number is a Ludic prime
Ludic numbers are formed by a sieve. Start with a list of the positive integers. Skip 1 and start with 2. Then delete every seco...

3 months ago

Solved

Find the closest canyon prime
My wife and I celebrated our honeymoon and most recent anniversary in Yellowstone and Grand Teton National Parks. After returnin...

3 months ago

Solved

Extend the digamma function to negative arguments
While solving one of Ramon Villamangca’s problems, I needed the value of , where is the digamma function. However, MATLAB’s fun...

3 months ago

Solved

Sum the reciprocals of polygonal numbers
As explained in Cody Problem 60571, a polygonal number is the number of dots arranged in the shape of a regular polygon. For exa...

3 months ago

Solved

Compute the totient summatory function
Cody Problem 656 deals with the totient function, denoted by which counts the numbers less than that are relatively prime to ....

3 months ago

Solved

Compute a sequence with the whyphi sieve
A few problems on Cody involve sieving. For example, Cody Problem 45367 involves the famous Sieve of Eratosthenes. CP 50811 uses...

3 months ago

Solved

Alert a city about a spill
Problem statement Cody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any muni...

3 months ago

Solved

Travel a path
In Cody Problem 60251, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, ...

3 months ago

Solved

Compute the Ramanujan tau function
The Ramanujan tau function is defined by the relation where . The first few values of are 1, -24, 252, -1472, and 4830. W...

3 months ago

Solved

List the segmented numbers
The sequence of segmented numbers begins 1, 2, 4, 5, 8, 10, 14, 15, 16. Notice that none of the terms is the sum of consecutive ...

3 months ago

Solved

List the ways to write 1/n as the sum of two unit fractions
Cody Problem 59841 involved counting the ways that can be written as the sum of two unit fractions (those with a numerator of 1...

3 months ago

Solved

Count the ways to write 1/n as the sum of two unit fractions
The number 1/2 can be written as 1/3+1/6 and 1/4+1/4, and the number 1/9 can be written as 1/18+1/18, 1/12+1/36, and 1/10+1/90. ...

3 months ago

Solved

Solve an ODE: Ekman spiral on a solid surface
Problem Write a function to solve for and as a function of in this system of ordinary differential equations: where , ...

3 months ago

Solved

Update course numbers and abbreviations
Suppose that the educational institution where you teach purchases new software to handle many essential functions, including co...

3 months ago

Solved

List ways to make a sum in Killer Sudoku
In Sudoku, the subject of several Cody problems, one tries to arrange the digits 1 through 9 in a 9x9 grid of 81 cells (or a 3x3...

3 months ago

Solved

Compute the polylogarithm for real arguments
The polylogarithm appears in quantum statistics and quantum electrodynamics, and for special cases of and , it connects to the...

3 months ago

Solved

Count paths between corners of a grid that remain on or below the diagonal
Consider motion from the lower left corner of a square grid to the upper right corner. The motion is constrained in two ways: (1...

3 months ago

Solved

Count the ones in a divisibility matrix
Cody Problem 59506 asked solvers to compute the determinant of matrix consisting of ones in the first column and anywhere the ro...

3 months ago

Solved

Compute the determinant of a divisibility matrix
Consider a matrix consisting of ones in the first column and anywhere the row index divides the column index. The 4x4 matrix is ...

3 months ago

Solved

Compute the sum of distances from a point to the sides of an equilateral triangle
Write a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the ...

3 months ago