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math.NT2010
On common values of and , II
Kevin Ford, Paul Pollack
Let phi(n) be Euler's totient function and let sigma(n) be the sum of the positive divisors of n. We show that most phi-values (integers in the range of phi) are not sigma-values a…
math.NT2010
On perfect and near-perfect numbers
Vladimir Shevelev
We call positive integer n a near-perfect number, if it is sum of all its proper divisors, except of one of them ("redundant divisor"). We prove an Euclid-like theorem for near-per…
math.NT2010
On common values of phi(n) and sigma(n), I
Kevin Ford, Paul Pollack
We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x(log x)^{-1+o(1)} numbers not exceeding x common to the ranges of Euler's function phi(n…