Abstract
Given an integer q≥2, we say that a positive integer is a q-Niven number if it is divisible by the sum of its digits in base q. Given an arbitrary integer r∈[2,2q], we say that (n,n+1,…,n+r−1) is a q-Niven r -tuple if each number n+i, for i=0,1,…,r−1, is a q-Niven number. We show that there exists a positive constant c=c(q,r) such that the number of q-Niven r-tuples whose leading component is <x is asymptotic to cx/(log x)r as x→∞.
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Research of J.M. De Koninck supported in part by a grant from NSERC.
Research of I. Kátai supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA.
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De Koninck, J.M., Doyon, N. & Kátai, I. Counting the number of twin Niven numbers. Ramanujan J 17, 89–105 (2008). https://doi.org/10.1007/s11139-008-9127-z
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DOI: https://doi.org/10.1007/s11139-008-9127-z