• Corpus ID: 203578307

ON A VARIATION OF PERFECT NUMBERS

@inproceedings{Iannucci2006ONAV,
  title={ON A VARIATION OF PERFECT NUMBERS},
  author={Douglas E. Iannucci},
  year={2006}
}
We define a positive integer n to be k-imperfect if kρ(n) = kn for some integer k ≥ 2. Here, ρ is a multiplicative arithmetic function defined by ρ(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for a prime power pa. We address three questions regarding k-imperfect numbers; in particular we find several necessary conditions for the existence of odd 3-imperfect numbers. 

On k-Imperfect Numbers

Abstract A positive integer n is called a k-imperfect number if kρ(n) = n for some integer k ⩾ 2, where ρ is a multiplicative arithmetic function defined by ρ(pa ) = pa – p a–1 + p a–2 – ⋯ + (–1) a

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