login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
MATHEMATICA
a[n_] := Module[{f, d, t, x = 0}, For[z = n+1, z <= Quotient[201*n, 100], z++, f = 1/n - 1/z; d = Denominator[f]; Do[t = (y/d + 1/y)/f; If[Denominator[t] == 1, x = Max[x, t*y]], {y, Divisors[d]}]]; x]; Table[a[n], {n, 1, 36}] (* Jean-François Alcover, Jul 10 2017, after Charles R Greathouse IV *)
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
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