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Feller–Tornier constant
From OeisWiki
The Feller–Tornier constant, named after William Feller (1906 –1970) and Erhard Tornier (1894 –1982), is^{[1]}^{[2]}

CFeller–Tornier =
1 +1 2 ∞∏ i = 1
=2 pi 2
1 +1 2 1 ζ (2) ∞∏ i = 1
=1 pi 2 − 1
,[ω (∑ ni = 1
) mod 2 = 0]i rad ( i ) n
ω (n) 
rad (n) 
n 
ζ (2) =

[·] 
Note: A065474 defines the Feller–Tornier constant as (MISTAKE?) .
 ∞
∏ i = 1
,2 pi 2
pi 
i 
Contents
Decimal expansion
A065474 Decimal expansion of

 {3, 2, 2, 6, 3, 4, 0, 9, 8, 9, 3, 9, 2, 4, 4, 6, 7, 0, 5, 7, 9, 5, 3, 1, 6, 9, 2, 5, 4, 8, 2, 3, 7, 0, 6, 6, 5, 7, 0, 9, 5, 0, 5, 7, 9, 6, 6, 5, 8, 3, 2, 7, 0, 9, 9, 6, 1, 8, 1, 1, ...}

 {6, 6, 1, 3, 1, 7, 0, 4, 9, 4, 6, 9, 6, 2, 2, 3, 3, 5, 2, 8, 9, 7, 6, 5, 8, 4, 6, 2, 7, 4, 1, 1, 8, 5, 3, 3, 2, 8, 5, 4, 7, 5, 2, 8, 9, 8, 3, 2, 9, 1, 6, 3, 5, 4, 9, 8, 0, 9, 0, 5, ...}
Continued fraction
The simple continued fraction for

 {0, 3, 10, 19, 2, 1, 2, 2, 1, 6, 1, 6, 19, 17, 1, 7, 1, 2, 2, 1, 10, 2, 6, 2, 1, 3, 2, 1, 21, 5, 1, 15, 1, 1, 4, 1, 1, 1, 443, 2, 1, 4, 3, 1, 1, 6, 26, 6, 2, 39, 4, 1, 2, 6, 1, 1, 2, 4, ...}

 {0, 1, 1, 1, 20, 9, 1, 2, 5, 1, 2, 3, 2, 3, 38, 8, 1, 16, 2, 2, 21, 1, 12, 1, 2, 1, 1, 2, 43, 2, 1, 32, 10, 3, 221, 1, 2, 9, 1, 1, 3, ...}
Density of integers with an even number of prime factors
The density of integers with an even number of prime factors is

=[Ω (i) mod 2 = 0]∑ ni = 1n
,1 2
Ω (n) 
[⋅] 

L (x) := ∑ n ≤ x
Density of integers with an even number of distinct prime factors
The density of integers with an even number of distinct prime factors is

= ?,[ω (i) mod 2 = 0]∑ ni = 1n
ω (n) 
[·] 
Sequences
A007674 Numbersn 
n 
n + 1 
 {1, 2, 5, 6, 10, 13, 14, 21, 22, 29, 30, 33, 34, 37, 38, 41, 42, 46, 57, 58, 61, 65, 66, 69, 70, 73, 77, 78, 82, 85, 86, 93, 94, 101, 102, 105, 106, 109, 110, 113, 114, 118, 122, 129, ...}
A003557 n divided by the largest squarefree divisor of n.
 {1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 1, 1, 16, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, ...}
Notes
 ↑ Pieter Moree, FellerTornier Constant 0.32263..., Some numbertheoretical constants, 1999.
 ↑ Steven R. Finch, Mathematical Constants. (Cf. FellerTornier constant.)
External links
 Weisstein, Eric W., FellerTornier Constant, from MathWorld—A Wolfram Web Resource.