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 A065473 Decimal expansion of the strongly carefree constant: product(1 - (3*p-2)/(p^3)), p prime >= 2). 11
 2, 8, 6, 7, 4, 7, 4, 2, 8, 4, 3, 4, 4, 7, 8, 7, 3, 4, 1, 0, 7, 8, 9, 2, 7, 1, 2, 7, 8, 9, 8, 3, 8, 4, 4, 6, 4, 3, 4, 3, 3, 1, 8, 4, 4, 0, 9, 7, 0, 5, 6, 9, 9, 5, 6, 4, 1, 4, 7, 7, 8, 5, 9, 3, 3, 6, 6, 5, 2, 2, 4, 3, 1, 3, 1, 9, 4, 3, 2, 5, 8, 2, 4, 8, 9, 1, 2, 6, 8, 2, 5, 5, 3, 7, 4, 2, 3, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also decimal expansion of the probability that an integer triple (x, y, z) is pairwise coprime. - Charles R Greathouse IV, Nov 14 2011 LINKS J. Arias de Reyna, R. Heyman, Counting Tuples Restricted by Pairwise Coprimality Conditions, J. Int. Seq. 18 (2015) 15.10.4 T. D. Browning, The divisor problem for binary cubic forms, arXiv:1006.3476 [math.NT], 2010. G. Niklasch, Some number theoretical constants: 1000-digit values G. Niklasch, Some number theoretical constants: 1000-digit values [cached copy] László Tóth, The probability that k positive integers are pairwise relatively prime, Fibonacci Quart., 40 (2002), 13-18. Eric Weisstein's World of Mathematics, Carefree Couple FORMULA Equals Prod_{p prime} (1 - 1/p)^2*(1 + 2/p). - Michel Marcus, Apr 16 2016 EXAMPLE 0.2867474284344787341078927127898384... MATHEMATICA digits = 100; NSum[-(2+(-2)^n)*PrimeZetaP[n]/n, {n, 2, Infinity}, NSumTerms -> 2 digits, WorkingPrecision -> 2 digits, Method -> "AlternatingSigns"] // Exp // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 11 2016 *) PROG (PARI) prodeuler(p=2, 1e7, t=1-1./p; t^2*(t+3/p)) \\ Charles R Greathouse IV, Nov 14 2011 CROSSREFS Cf. A078073. Sequence in context: A021890 A199504 A019914 * A054029 A197589 A124356 Adjacent sequences:  A065470 A065471 A065472 * A065474 A065475 A065476 KEYWORD cons,nonn AUTHOR N. J. A. Sloane, Nov 19 2001 EXTENSIONS Name corrected by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 03 2003 STATUS approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)