Write a function to find integers n less than or equal to an input value m that solve the equation sigma(n-1) = phi(n+1). The function sigma(x) gives the sum of divisors of x; for example, sigma(15) = 1+3+5+15 = 24. The totient function phi(x) counts numbers less than x that are relatively prime to x. For example, phi(15) = 8 because 1, 2, 4, 7, 8, 11, 13, and 14 are relatively prime to 15; that is, the greatest common divisor of 15 and each of the eight numbers is 1.
An oblique hint is that I call solutions to sigma(n-1) = phi(n+1) “Beatriz numbers” in honor of a good friend and former co-worker of EmilyR and JessicaR. The natural search will not help, unless you are interested in combinatorics related to Higham’s conjecture.
Solve

Solution Stats

20 Solutions

10 Solvers

Last Solution submitted on May 25, 2026

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers10

Chris Cleveland Christian Schröder GeeTwo Hong Son

Suggested Problems

More from this Author326

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!