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              <text>Flora, Jeba S.; Roy, Anirban; Saikia, Manjil P.</text>
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              <text>On k-Facile Perfect Numbers</text>
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              <text>Springer Proceedings in Mathematics and Statistics;Volume;474;pp.111-121</text>
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              <text>Flora J.S., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India; Roy A., Department of Sciences and Humanities, CHRIST (Deemed to be University), Bangalore, India; Saikia M.P., Mathematical and Physical Sciences Division, School of Arts and Sciences, Ahmedabad University, Gujarat, Navrangpura, Ahmedabad, 380009, India</text>
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              <text>For a positive integer n, let ?(n) denote the sum of all positive divisors of n. Then n is said to be a k-facile perfect number if ?(n) = 2n + d1d2    dk, where 1 &amp;lt; d1, d2,, dk &amp;lt; n are distinct divisors of n. This paper characterizes k-facile perfect numbers and establishes their relationships with other special numbers.  The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.</text>
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              <text>Facile-perfect number; Near-perfect number; Perfect number</text>
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              <text>ISSN: 21941009; ISBN: 978-981976797-7;</text>
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              <text>Restricted Access; Hardcopy may be available in the library</text>
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