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Odd Repdigits to Small Bases Are Not Perfect

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Published/Copyright: October 2, 2012
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Integers
From the journal Integers Volume 12 Issue 5

Abstract.

We demonstrate, by considering each base in the range 2 through 9, that no odd repdigit with a base in that range is a perfect number.

Keywords: Perfect; Repdigit; Base
Received: 2010-08-12
Revised: 2011-09-14
Accepted: 2012-04-12
Published Online: 2012-10-02
Published in Print: 2012-10-01

© 2012 by Walter de Gruyter Berlin Boston

Articles in the same Issue

  1. Masthead
  2. Two-Color Babylon
  3. On Abelian and Additive Complexity in Infinite Words
  4. Approximations of Additive Squares in Infinite Words
  5. The Googol-th Bit of the Erdős–Borwein Constant
  6. Odd Repdigits to Small Bases Are Not Perfect
  7. Enumeration of the Degree Sequences of Line-Hamiltonian Multigraphs
  8. The Characteristic Sequence and p-Orderings of the Set of d-th Powers of Integers
  9. Van der Waerden's Theorem on Homothetic Copies of {1,1+s,1+s+t}
  10. Sum-Products Estimates with Several Sets and Applications
  11. The 2-Adic, Binary and Decimal Periods of 1/3k Approach Full Complexity for Increasing k
  12. A Proof of Catalan's Convolution Formula
  13. Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
  14. The Impossibility of Certain Types of Carmichael Numbers
  15. Integer Subsets with High Volume and Low Perimeter
  16. Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
  17. A Generalized Diagonal Wythoff Nim
  18. A Recursive Process Related to a Partizan Variation of Wythoff
  19. The (r1,...,rp)-Stirling Numbers of the Second Kind
  20. Factor Frequencies in Languages Invariant Under Symmetries Preserving Factor Frequencies
  21. On k-Lehmer Numbers
https://doi.org/10.1515/integers-2012-0008
Keywords for this article
Perfect; Repdigit; Base

Articles in the same Issue

  1. Masthead
  2. Two-Color Babylon
  3. On Abelian and Additive Complexity in Infinite Words
  4. Approximations of Additive Squares in Infinite Words
  5. The Googol-th Bit of the Erdős–Borwein Constant
  6. Odd Repdigits to Small Bases Are Not Perfect
  7. Enumeration of the Degree Sequences of Line-Hamiltonian Multigraphs
  8. The Characteristic Sequence and p-Orderings of the Set of d-th Powers of Integers
  9. Van der Waerden's Theorem on Homothetic Copies of {1,1+s,1+s+t}
  10. Sum-Products Estimates with Several Sets and Applications
  11. The 2-Adic, Binary and Decimal Periods of 1/3k Approach Full Complexity for Increasing k
  12. A Proof of Catalan's Convolution Formula
  13. Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
  14. The Impossibility of Certain Types of Carmichael Numbers
  15. Integer Subsets with High Volume and Low Perimeter
  16. Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
  17. A Generalized Diagonal Wythoff Nim
  18. A Recursive Process Related to a Partizan Variation of Wythoff
  19. The (r1,...,rp)-Stirling Numbers of the Second Kind
  20. Factor Frequencies in Languages Invariant Under Symmetries Preserving Factor Frequencies
  21. On k-Lehmer Numbers
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