Journal of Integer Sequences, Vol. 26 (2023), Article 23.9.1

Product of Some Polynomials and Arithmetic Functions


Passawan Noppakaew
Department of Mathematics
Faculty of Science
Silpakorn University
Nakhon Pathom, 73000
Thailand

Prapanpong Pongsriiam
Department of Mathematics
Faculty of Science
Silpakorn University
Nakhon Pathom, 73000
Thailand
and
Graduate School of Mathematics
Nagoya University
Nagoya, 464-8602
Japan

Abstract:

We study the injectivity and noninjectivity of the function fg, where f is a polynomial in a simple form and g is a popular arithmetic function such as the Euler totient function or the sum of divisors function. We also show the connection between our results and Mersenne primes, amicable pairs, and other integer sequences.

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(Concerned with sequences A000010 A000396 A000668 A001065 A002025 A002046 A007617 A008888 A038040 A063900 A063990 A064097 A064987 A098007 A212327 A212490 A259180 A337873 A338382.)

Received December 13 2022; revised version received April 10 2023. Published in Journal of Integer Sequences, November 2 2023.

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