On exponentially perfect numbers relatively prime to 15

Kolenick, Joseph F.

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dc.contributor.author	Kolenick, Joseph F.
dc.contributor.other	Youngstown State University. Department of Mathematics.
dc.date.accessioned	2021-10-15T15:43:56Z
dc.date.available	2021-10-15T15:43:56Z
dc.date.issued	2007
dc.identifier.other	B20254386
dc.identifier.other	226291144
dc.identifier.uri	https://jupiter.ysu.edu:443/record=b2025438
dc.identifier.uri	http://hdl.handle.net/1989/16632
dc.description	iii, 12 leaves : ill. ; 29 cm. Thesis (M.S.)--Youngstown State University, 2007. Includes bibliographical references (leaf 10).	en_US
dc.description.abstract	If the natural number n has the canonical form p1a1p2a2⋯prar, then we say that an exponential divisor of n has the form d = p1b1p2b2⋯prbr, where bi\|ai for i = 1, 2, … r. We denote the sum of the exponential divisors of n by σ(e)(n). A natural number n is said to be exponentially perfect (or e-perfect) if σ(e)(n) = 2n. The purpose of this thesis is to investigate the existence of e-perfect numbers relatively prime to 15. In particular, if such numbers exist, are they bounded below? How many distinct prime divisors must they have? Several lemmas are utilized throughout the paper on route to answering these questions. Also, computer programs written in Maple are used for numerical estimates.	en_US
dc.description.sponsorship	Youngstown State University. Department of Mathematics.	en_US
dc.language.iso	en_US	en_US
dc.relation.ispartofseries	Master's Theses;no. 0973
dc.subject	Mathematics.	en_US
dc.title	On exponentially perfect numbers relatively prime to 15	en_US
dc.type	Thesis	en_US

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