Logarithm

Algebra Level 3

Find the smallest positive integer kk such that 1log3k2015!+1log4k2015!++1log2015k2015!>2015\dfrac{1}{\log_{3^k}2015!}+\dfrac{1}{\log_{4^k}2015!}+\ldots+\dfrac{1}{\log_{2015^k}2015!}>2015

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