Alternating Sums Concerning Multiplicative Arithmetic Functions
László Tóth
Department of Mathematics
University of Pécs
Ifjúság útja 6
7624 Pécs
Hungary
Abstract:
We deduce asymptotic formulas for the alternating sums
and
,
where
f is one of the following classical
multiplicative arithmetic functions: Euler's totient function, the Dedekind function, the sum-of-divisors
function, the divisor function, the gcd-sum function. We also consider analogs of these functions, which are
associated to unitary and exponential divisors, and other special functions. Some of our results improve the error
terms obtained by Bordellès and Cloitre. We formulate certain open problems.
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(Concerned with sequences
A000005
A000010
A000041
A000203
A000688
A001615
A002088
A005117
A006218
A007947
A013928
A018804
A024916
A033999
A034448
A047994
A048651
A049419
A057521
A063966
A064609
A065442
A065463
A068762
A068773
A084911
A143348
A145353
A173290
A177754
A188999
A206369
A272718.)
Received August 4 2016; revised versions received October 20 2016; December 13 2016.
Published in Journal of Integer Sequences, December 27 2016.
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