login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082986 Largest x such that 1/x + 1/y + 1/z = 1/n. 5
6, 42, 156, 420, 930, 1806, 3192, 5256, 8190, 12210, 17556, 24492, 33306, 44310, 57840, 74256, 93942, 117306, 144780, 176820, 213906, 256542, 305256, 360600, 423150, 493506, 572292, 660156, 757770, 865830, 985056, 1116192, 1260006, 1417290, 1588860, 1775556 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The greedy algorithm gives the decomposition 1/n = 1/(n+1) + 1/(n^2+n+1) + 1/(n^4+2n^3+2n^2+n). - Charles R Greathouse IV, Oct 17 2012

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..5000

FORMULA

a(n) >= n^4 + 2n^3 + 2n^2 + n (cf. A169938). - Charles R Greathouse IV, Oct 17 2012. [Note this is at present only a lower bound! - N. J. A. Sloane, Jan 27 2014]

a(n) >= 6*A006325(n-1). -  Robert G. Wilson v, May 04 2013 [Corrected by Michael Somos, Jan 27 2014]

a(n) < 3*n^4 for n>=2 (upper bound). - Carmine Suriano, Feb 20 2014

PROG

(PARI) a(n)=my(f, d, t, x); for(z=n+1, 201*n\100, f=1/n-1/z; d=denominator(f); fordiv(d, y, t=(y/d+1/y)/f; if(denominator(t)==1, x=max(x, t*y)))); x \\ Charles R Greathouse IV, Oct 17 2012

CROSSREFS

Cf. A082604, A006325, A169938.

Sequence in context: A199905 A176780 A169938 * A180806 A253946 A062136

Adjacent sequences:  A082983 A082984 A082985 * A082987 A082988 A082989

KEYWORD

nonn,nice

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), May 29 2003

EXTENSIONS

a(6)-a(36) from Charles R Greathouse IV, Oct 17 2012

Deleted incorrect (or at least unproved) Mma program. - N. J. A. Sloane, Jan 27 2014

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.