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A082695
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Decimal expansion of zeta(2)*zeta(3)/zeta(6).
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6
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1, 9, 4, 3, 5, 9, 6, 4, 3, 6, 8, 2, 0, 7, 5, 9, 2, 0, 5, 0, 5, 7, 0, 7, 0, 3, 6, 2, 5, 7, 4, 7, 6, 3, 4, 3, 7, 1, 8, 7, 8, 5, 8, 5, 0, 1, 7, 6, 7, 8, 0, 5, 7, 1, 6, 0, 2, 6, 6, 3, 5, 6, 8, 8, 9, 0, 0, 5, 3, 4, 9, 5, 0, 6, 9, 3, 5, 5, 4, 0, 5, 3, 9, 4, 8, 1, 7, 9, 1, 0, 0, 8, 2, 1, 1, 1, 1, 3, 0, 1, 0, 6, 9, 0, 5
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OFFSET
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1,2
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COMMENTS
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Equals the Dirichlet zeta-function sum_{n>=1} A001615(n)/n^s at s=3. - R. J. Mathar, Apr 02 2011.
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REFERENCES
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S. W. Golomb, Powerful numbers, Amer. Math. Monthly, Vol. 77 (1970), 848-852.
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LINKS
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Table of n, a(n) for n=1..105.
J. von Zur Gathen et al., Average order in cyclic groups, J. Theor. Nombres Bordeaux, 16 (2004), 107-123. Lists several other papers where this constant arises.
Eric Weisstein's World of Mathematics, Totient Summatory Function
Eric Weisstein's World of Mathematics, Powerful Number
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FORMULA
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Decimal expansion of product( 1+1/p/(p-1), for all prime p) = zeta(2)*zeta(3)/zeta(6)=1.94359643682075920505707...
The sum of the reciprocals of the powerful numbers, A001694. - T. D. Noe, May 03 2006
Equals A013661 * A002117 / A013664 = 1/ A068468 = zeta(3) * 315/(2*pi^4) = zeta(3) * A157292.
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EXAMPLE
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1.9435964368207592...
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MATHEMATICA
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First@RealDigits[ Zeta[2]*Zeta[3]/Zeta[6], 10, 100]
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CROSSREFS
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Cf. A014197, A070243, A082696 (continued fraction).
Sequence in context: A021110 A010540 A187466 * A019909 A117018 A193712
Adjacent sequences: A082692 A082693 A082694 * A082696 A082697 A082698
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KEYWORD
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cons,nonn
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AUTHOR
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Benoit Cloitre, Apr 12 2003
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EXTENSIONS
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New definition from Eric W. Weisstein, May 04 2006
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STATUS
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approved
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