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   A060797 Integer part of square root of n-th primorial, A002110(n). 9
   1, 1, 2, 5, 14, 48, 173, 714, 3114, 14936, 80434, 447839, 2724103, 17442771, 114379899, 784149081, 5708691485, 43849291330, 342473913399, 2803269796341, 23620771158594, 201815957246321, 1793779464521955, 16342108667160301, 154171144824008979 (list; graph; refs; listen; history; text; internal format)
   OFFSET 0,3 COMMENTS Integer part of square root of product of n first primes. LINKS FORMULA a(n) = A000196(A002110(n)) = floor(sqrt(A002110(n))) EXAMPLE n=8, q(8)=2.3.5.7.11.13.17.19=9699690, a(8)=3114. This is between 128th and 129th divisors of 8th primorial: 3094 < A000196(9699690)=3114 < 3135. (In general, A000196(n) has always 2^n divisors, and A000196(x) is always comprised between the k-th and (k+1)-th divisor of n, where k=ceil(tau(x)/2), tau(x) being the number of divisors of x.) - M. F. Hasler, Sep 02 2012 MATHEMATICA a = {}; Do[b = 1; Do[b = b Prime[x], {x, 1, n}]; AppendTo[a, Floor[b^(1/2)]], {n, 1, 100}]; a (* Artur Jasinski *) PROG (PARI) A060797(n)=sqrtint(prod(k=1, n, prime(k))) \\ - M. F. Hasler, Sep 02 2012 CROSSREFS Cf. A002110, A060797, A127600. Sequence in context: A149905 A149906 A129778 * A124381 A131236 A119499 Adjacent sequences:  A060794 A060795 A060796 * A060798 A060799 A060800 KEYWORD nonn AUTHOR Labos Elemer, Apr 27 2001 EXTENSIONS a(23) correction by Hans Havermann, Dec 02 2010 Extended to a(0)=1=sqrt(A002110(0)) by M. F. Hasler, Sep 02 2012 STATUS approved
  
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explanation: The provided text is an excerpt from the Online Encyclopedia of Integer Sequences (OEIS) describing the sequence A060797. This sequence represents the integer part of the square root of the n-th primorial, which is the product of the first n prime numbers. The text includes a definition, comments, a formula, an example, Mathematica and PARI code for generating the sequence, and cross-references to related sequences. It does not contain a specific question or a question and answer.
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: This site is supported by donations to The OEIS Foundation.
  
   Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate
  
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   A060797 Integer part of square root of n-th primorial, A002110(n). 9
   1, 1, 2, 5, 14, 48, 173, 714, 3114, 14936, 80434, 447839, 2724103, 17442771, 114379899, 784149081, 5708691485, 43849291330, 342473913399, 2803269796341, 23620771158594, 201815957246321, 1793779464521955, 16342108667160301, 154171144824008979 (list; graph; refs; listen; history; text; internal format)
   OFFSET 0,3 COMMENTS Integer part of square root of product of n first primes. LINKS FORMULA a(n) = A000196(A002110(n)) = floor(sqrt(A002110(n))) EXAMPLE n=8, q(8)=2.3.5.7.11.13.17.19=9699690, a(8)=3114. This is between 128th and 129th divisors of 8th primorial: 3094 < A000196(9699690)=3114 < 3135. (In general, A000196(n) has always 2^n divisors, and A000196(x) is always comprised between the k-th and (k+1)-th divisor of n, where k=ceil(tau(x)/2), tau(x) being the number of divisors of x.) - M. F. Hasler, Sep 02 2012 MATHEMATICA a = {}; Do[b = 1; Do[b = b Prime[x], {x, 1, n}]; AppendTo[a, Floor[b^(1/2)]], {n, 1, 100}]; a (* Artur Jasinski *) PROG (PARI) A060797(n)=sqrtint(prod(k=1, n, prime(k))) \\ - M. F. Hasler, Sep 02 2012 CROSSREFS Cf. A002110, A060797, A127600. Sequence in context: A149905 A149906 A129778 * A124381 A131236 A119499 Adjacent sequences:  A060794 A060795 A060796 * A060798 A060799 A060800 KEYWORD nonn AUTHOR Labos Elemer, Apr 27 2001 EXTENSIONS a(23) correction by Hans Havermann, Dec 02 2010 Extended to a(0)=1=sqrt(A002110(0)) by M. F. Hasler, Sep 02 2012 STATUS approved
  
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an excerpt from the Online Encyclopedia of Integer Sequences (OEIS) describing the sequence A060797. This sequence represents the integer part of the square root of the n-th primorial, which is the product of the first n prime numbers. The text includes a definition, comments, a formula, an example, Mathematica and PARI code for generating the sequence, and cross-references to related sequences. It does not contain a specific question or a question and answer.
  
  Label: no-question