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math.NT2017
Shifts of the prime divisor function of Alladi and Erdős
Snehal Shekatkar, Tian An Wong
We introduce a variation on the prime divisor function of Alladi and Erdős, a close relative of the sum of proper divisors function . After proving some basic properti…
math.NT2017★ 3 cited
Biases in prime factorizations and Liouville functions for arithmetic progressions
Peter Humphries, Snehal M. Shekatkar, Tian An Wong
We introduce a refinement of the classical Liouville function to primes in arithmetic progressions. Using this, we discover new biases in the appearances of primes in a given arith…