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A065473 Decimal expansion of the strongly carefree constant: product(1 - (3*p-2)/(p^3)), p prime >= 2). 8
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

Table of n, a(n) for n=0..97.

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 December 10 21:23 EST 2016. Contains 279011 sequences.