login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082020 Decimal expansion of 15/Pi^2. 21
1, 5, 1, 9, 8, 1, 7, 7, 5, 4, 6, 3, 5, 0, 6, 6, 5, 7, 1, 6, 5, 8, 1, 9, 1, 9, 4, 8, 1, 4, 5, 9, 1, 4, 5, 8, 3, 5, 6, 5, 3, 8, 1, 6, 2, 0, 0, 8, 3, 6, 9, 8, 2, 3, 2, 6, 8, 4, 1, 3, 5, 4, 7, 8, 4, 1, 2, 5, 9, 6, 8, 1, 4, 4, 3, 3, 5, 3, 1, 6, 1, 7, 8, 6, 8, 1, 3, 9, 1, 0, 8, 8, 8, 4, 3, 2, 7, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

3/(2*Pi^2) (the same decimal expansion with an offset 0) is the probability that the greatest common divisor of two numbers selected at random is 2 (Christopher, 1956). - Amiram Eldar, May 23 2020

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

John Christopher, The Asymptotic Density of Some k-Dimensional Sets, The American Mathematical Monthly, Vol. 63, No. 6 (1956), pp. 399-401.

Werner Hürlimann, Dedekind's arithmetic function and primitive four squares counting functions, Journal of Algebra, Number Theory: Advances and Applications, Vol. 14, No. 2 (2015), pp. 73-88.

S. Ramanujan, Irregular numbers, J. Indian Math. Soc., Vol. 5 (1913), pp. 105-106.

V. Sitaramaiah and M. V. Subbarao, Some asymptotic formulae involving powers of arithmetic functions, Number Theory, Madras 1987, Springer, 1989, pp. 201-234, alternative link (p. 230).

Eric Weisstein's World of Mathematics, Prime Sums

Eric Weisstein's World of Mathematics, Moebius Function

Eric Weisstein's World of Mathematics, Prime Products

Index entries for transcendental numbers

FORMULA

Product_{n >= 1} (1+1/prime(n)^2) = 15/Pi^2. - Ramanujan

Equals Zeta(2)/Zeta(4) = A013661/A013662 = Sum_{n>=1} mu(n)^2/n^2 = Sum_{n>=1} |mu(n)|/n^2 . - Enrique Pérez Herrero, Jan 15 2012

Equals Sum_{n>=1} 1/A005117(n)^2 . - Enrique Pérez Herrero, Mar 30 2012

Equals lim_{n->oo} (1/n) * Sum_{k=1..n} psi(k)/k, where psi(k) is the Dedekind psi function (A001615) - Amiram Eldar, May 12 2019.

EXAMPLE

1.51981775463506657...

MAPLE

evalf(15/Pi^2, 120); # G. C. Greubel, Oct 18 2019

MATHEMATICA

A082020[digits_] := First[RealDigits[Zeta[2]/Zeta[4], 10, digits]]; A082020[100] (* Enrique Pérez Herrero, Jan 15 2012 *)

RealDigits[15/Pi^2, 10, 120][[1]] (* Harvey P. Dale, Jun 23 2019 *)

PROG

(PARI) 15/Pi^2 \\ Michel Marcus, Oct 18 2019

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); 15/Pi(R)^2; // G. C. Greubel, Oct 18 2019

(Sage) numerical_approx(15/pi^2, digits=100) # G. C. Greubel, Oct 18 2019

CROSSREFS

Cf. A001615, A157290.

Sequence in context: A154605 A114594 A021662 * A256559 A182498 A147406

Adjacent sequences:  A082017 A082018 A082019 * A082021 A082022 A082023

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, May 09 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 16:50 EDT 2021. Contains 343156 sequences. (Running on oeis4.)