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A215267
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Decimal expansion of 90/Pi^4.
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15
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9, 2, 3, 9, 3, 8, 4, 0, 2, 9, 2, 1, 5, 9, 0, 1, 6, 7, 0, 2, 3, 7, 5, 0, 4, 9, 4, 0, 4, 0, 6, 8, 2, 4, 7, 2, 7, 6, 4, 5, 0, 2, 1, 6, 6, 8, 2, 7, 4, 4, 3, 6, 4, 4, 6, 3, 5, 1, 2, 3, 1, 9, 2, 4, 7, 7, 6, 2, 9, 6, 4, 0, 7, 9, 9, 6, 7, 2, 8, 2, 2, 4, 1, 6, 5, 1, 4, 3, 7, 3, 6, 5, 7, 6, 1, 4, 4, 1, 5
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OFFSET
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0,1
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COMMENTS
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Decimal expansion of 1/zeta(4), the inverse of A013662. This is the probability that 4 randomly chosen natural numbers are relatively prime.
Also the asymptotic probability that a random integer is 4-free. See equivalent comments in A088453, A059956. - Balarka Sen, Aug 08 2012
The probability that the greatest common divisor of two numbers selected at random is squarefree (Christopher, 1956). - Amiram Eldar, May 23 2020
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 231.
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LINKS
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FORMULA
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1/zeta(4) = 90/Pi^4 = Product_{k>=1} (1 - 1/prime(k)^4) = Sum_{n>=1} mu(n)/n^4, a Dirichlet series for the Möbius function mu. See the examples in Apostol, here for s = 4. - Wolfdieter Lang, Aug 07 2019
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EXAMPLE
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0.92393840292159016702375049404068247276450216682744364463512319...
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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