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- Carl Pomerance, Hee-Sung Yang
- Math. Comput.
- 2014

In 1973, Erdős proved that a positive proportion of numbers are not of the form σ(n) − n, the sum of the proper divisors of n. We prove the analogous result where σ is replaced with the sum-of-unitary-divisors function σ∗ (which sums divisors d of n such that (d, n/d) = 1), thus solving a problem of te Riele from 1976. We also describe a fast algorithm for… (More)

- Odeny Nazarius Koyi, Hee-Sung Yang, Youngmi Kwon
- CSOC
- 2015

In 1973, Erdős proved that a positive proportion of numbers are untouchable; that is, not of the form s(n), where s(n) := σ(n)−n is the sum of the proper divisors of n. We investigate the analogous question where σ is replaced with similar divisor functions, such as the unitary sum-of-divisors function σ∗ (which sums those divisors d of n co-prime to n/d).… (More)

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