Arithmetic functions associated with infinitary divisors of an integer
The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y. In this paper, we investigate the infinitary analogues of such familiar number theoretic function...
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171293000456 |
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| _version_ | 1832566135405412352 |
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| author | Graeme L. Cohen Peter Hagis |
| author_facet | Graeme L. Cohen Peter Hagis |
| author_sort | Graeme L. Cohen |
| collection | DOAJ |
| description | The infinitary divisors of a natural number n are the products of its divisors of
the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1)
is the binary representation of y. In this paper, we investigate the infinitary analogues of such
familiar number theoretic functions as the divisor sum function, Euler's phi function and the
Möbius function. |
| format | Article |
| id | doaj-art-66ba50681e0844e1b0f23ae04baf58e5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-66ba50681e0844e1b0f23ae04baf58e52025-02-03T01:04:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116237338310.1155/S0161171293000456Arithmetic functions associated with infinitary divisors of an integerGraeme L. Cohen0Peter Hagis1School of Mathematical Sciences, University of Technology, Broadway, Sydney 2007, NSW, AustraliaSchool of Mathematical Sciences, University of Technology, Broadway, Sydney 2007, NSW, AustraliaThe infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y. In this paper, we investigate the infinitary analogues of such familiar number theoretic functions as the divisor sum function, Euler's phi function and the Möbius function.http://dx.doi.org/10.1155/S0161171293000456infinitary divisorsarithmetic functionsinfinitary convolutions asymptotic formulae. |
| spellingShingle | Graeme L. Cohen Peter Hagis Arithmetic functions associated with infinitary divisors of an integer International Journal of Mathematics and Mathematical Sciences infinitary divisors arithmetic functions infinitary convolutions asymptotic formulae. |
| title | Arithmetic functions associated with infinitary divisors of an integer |
| title_full | Arithmetic functions associated with infinitary divisors of an integer |
| title_fullStr | Arithmetic functions associated with infinitary divisors of an integer |
| title_full_unstemmed | Arithmetic functions associated with infinitary divisors of an integer |
| title_short | Arithmetic functions associated with infinitary divisors of an integer |
| title_sort | arithmetic functions associated with infinitary divisors of an integer |
| topic | infinitary divisors arithmetic functions infinitary convolutions asymptotic formulae. |
| url | http://dx.doi.org/10.1155/S0161171293000456 |
| work_keys_str_mv | AT graemelcohen arithmeticfunctionsassociatedwithinfinitarydivisorsofaninteger AT peterhagis arithmeticfunctionsassociatedwithinfinitarydivisorsofaninteger |