We study several problems in the field of modified divisors; more precisely, from the theory of exponential and infinitary divisors. We analyze the behavior of modified divisors, sum-of-divisors, and totient functions. Our main results are connected with the asymptotic behavior of mean values and explicit estimates of the extreme orders for these functions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 8, pp. 1068–1079, August, 2016.
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Lelechenko, A. Exponential and Infinitary Divisors. Ukr Math J 68, 1222–1237 (2017). https://doi.org/10.1007/s11253-017-1289-7
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DOI: https://doi.org/10.1007/s11253-017-1289-7