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   A308219 Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions. 3
  
  %I
  
  %S 2,4,5,7,6,10,6,11,10,12,8,17,6,13,14,16,8,20,8,21,17,14,10,27,12,15,
  
  %T 18,23,10,29,8,23,18,17,20,34,6,17,20,33,10,34,8,25,28,17,12,41,14,27,
  
  %U 20,27,10,35,24,36,21,18,14,51,6,18,33,32,22,36,8,30,25,39,14,54,6,17,33,30,25,39,12,49,28,18,14,60,22,19,25,39,14,58,20,29,21,21,24,59,8,32,36,48
  
  %N Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions.
  
  %C a(n) is the number of fractions of denominator n which are the sum of two unit fractions: m/n = 1/r + 1/s (m and n not necessarily coprime).
  
  %H Cyril Banderier, Florian Luca, Francesco Pappalardi, <a href="https://lipn.fr/~cb/Papers/EgyptianFractions.pdf">Numerators of Egyptian fractions</a>, 2019.
  
  %F For p prime, a(p) = 2 + tau(p+1) with tau = A000005.
  
  %e a(2)=4, as there are 4 fractions with denominator 4 which are the sums of 2 unit fractions: 1/2 = 1/4 + 1/4, 2/2 = 1/2 + 1/2, 3/2 = 1/1 + 1/2, 4/2 = 1/1 + 1/1.
  
  %Y Cf. A000005, A308220, A308221, A308415.
  
  %K nonn
  
  %O 1,1
  
  %A _Cyril Banderier_, May 15 2019
  
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  Last modified January 21 21:20 EST 2022. Contains 350480 sequences. (Running on oeis4.)
explanation: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS). It describes a sequence (A308219) that represents the number of Egyptian fractions of a given denominator which can be expressed as the sum of two unit fractions. The entry includes the sequence definition, initial terms, a formula, an example, and references to related sequences. The text does not contain a specific question or a question-and-answer pair.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: The OEIS is supported by the many generous donors to the OEIS Foundation.
  
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   A308219 Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions. 3
  
  %I
  
  %S 2,4,5,7,6,10,6,11,10,12,8,17,6,13,14,16,8,20,8,21,17,14,10,27,12,15,
  
  %T 18,23,10,29,8,23,18,17,20,34,6,17,20,33,10,34,8,25,28,17,12,41,14,27,
  
  %U 20,27,10,35,24,36,21,18,14,51,6,18,33,32,22,36,8,30,25,39,14,54,6,17,33,30,25,39,12,49,28,18,14,60,22,19,25,39,14,58,20,29,21,21,24,59,8,32,36,48
  
  %N Number of Egyptian fractions of denominator n which are the sum of 2 unit fractions.
  
  %C a(n) is the number of fractions of denominator n which are the sum of two unit fractions: m/n = 1/r + 1/s (m and n not necessarily coprime).
  
  %H Cyril Banderier, Florian Luca, Francesco Pappalardi, <a href="https://lipn.fr/~cb/Papers/EgyptianFractions.pdf">Numerators of Egyptian fractions</a>, 2019.
  
  %F For p prime, a(p) = 2 + tau(p+1) with tau = A000005.
  
  %e a(2)=4, as there are 4 fractions with denominator 4 which are the sums of 2 unit fractions: 1/2 = 1/4 + 1/4, 2/2 = 1/2 + 1/2, 3/2 = 1/1 + 1/2, 4/2 = 1/1 + 1/1.
  
  %Y Cf. A000005, A308220, A308221, A308415.
  
  %K nonn
  
  %O 1,1
  
  %A _Cyril Banderier_, May 15 2019
  
  Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
  Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
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  Last modified January 21 21:20 EST 2022. Contains 350480 sequences. (Running on oeis4.)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS). It describes a sequence (A308219) that represents the number of Egyptian fractions of a given denominator which can be expressed as the sum of two unit fractions. The entry includes the sequence definition, initial terms, a formula, an example, and references to related sequences. The text does not contain a specific question or a question-and-answer pair.
  
  Label: no-question