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math.NT2013★ 7 cited
Some normal numbers generated by arithmetic functions
Paul Pollack, Joseph Vandehey
Let . A real number is said to be g-normal if its base g expansion contains every finite sequence of digits with the expected limiting frequency. Let ϕdenote Euler's toti…
math.NT2013★ 2 cited
Variations on a theorem of Davenport concerning abundant numbers
Emily Jennings, Paul Pollack, Lola Thompson
Let σ(n) = \sum_{d \mid n}d be the usual sum-of-divisors function. In 1933, Davenport showed that that n/σ(n) possesses a continuous distribution function. In other words, the limi…