Abstract
A generalized formula is obtained for the sum of inverses of the prime counting function for a large class of arithmetical functions related to the iterated logarithms.
Highlights
AND MAIN RESULTLet π(x) be the number of primes not exceeding x
A generalized formula is obtained for the sum of inverses of the prime counting function for a large class of arithmetical functions related to the iterated logarithms
Bencherif [1] derived an asymptotic formula for the sum of reciprocals of a large class of arithmetic functions having the following expansion f (n) a1 log(n) am−1 logm−1(n)
Summary
AND MAIN RESULTLet π(x) be the number of primes not exceeding x. A generalized formula is obtained for the sum of inverses of the prime counting function for a large class of arithmetical functions related to the iterated logarithms. Where m ≥ 1 and {kj}j is the sequence of integers given by the recurrence relation kn + 1! Asymptotic expansion, arithmetical function, prime number theorem.
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