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Refactorable number

A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that τ ( n ) ∣ n {\displaystyle \tau (n)\mid n} with τ ( n ) = σ 0 ( n ) = ∏ i = 1 n ( e i + 1 ) {\displaystyle \tau (n)=\sigma _{0}(n)=\prod _{i=1}^{n}(e_{i}+1)} for n = ∏ i = 1 n p i e i {\displaystyle n=\prod…

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Overview

  • Divisors Divisor
  • OEIS On-Line Encyclopedia of Integer Sequences
  • 12 12 (number)
  • 18 18 (number)
  • 24 24 (number)
  • 36 36 (number)
  • 40 40 (number)
  • 56 56 (number)
  • 60 60 (number)
  • 72 72 (number)
  • 80 80 (number)
  • 84 84 (number)
  • 88 88 (number)
  • 96 96 (number)
  • 104 104 (number)
  • 108 108 (number)
  • 128 128 (number)
  • 132 132 (number)
  • 136 136 (number)
  • 152 152 (number)
  • 156 156 (number)
  • 180 180 (number)
  • 184 184 (number)
  • 204 204 (number)
  • 225 225 (number)
  • 228 228 (number)
  • 232 232 (number)
  • 240 240 (number)
  • 248 248 (number)
  • 252 252 (number)

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History

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Map overview Semantic statistics

Refactorable number

Nodes45
Edges44
Triples18
Avg. degree1.96
Density0.044444
Components1

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Refactorable number

Top relations

related to history · 9
Refactorable number → Colton, Cooper, Curtis Cooper, First, HR, Kennedy, Robert, Simon Colton, While
related to Properties · 7
Refactorable number → Colton, Cooper, Kennedy, Let, Spiro, The, Zelinsky

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Important terminology

refactorable numbers displaystyle number colton divisors proved tau first divisible cooper kennedy infinitely many a033950 oeis 18 natural density zero

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
number theoryinstance ofwhich invents and judges definitions from a variety of areas of mathematics0.80text
graph theoryinstance ofwhich invents and judges definitions from a variety of areas of mathematics0.80text
Refactorable numberrelated to historyFirst0.60section
Refactorable numberrelated to historyCurtis Cooper0.60section
Refactorable numberrelated to historyRobert0.60section
Refactorable numberrelated to historyKennedy0.60section
Refactorable numberrelated to historySimon Colton0.60section
Refactorable numberrelated to historyHR0.60section
Refactorable numberrelated to historyColton0.60section
Refactorable numberrelated to historyWhile0.60section
Refactorable numberrelated to historyCooper0.60section
Refactorable numberrelated to PropertiesCooper0.60section

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    Min side: 3
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