

A078173


Max[min(r,s,t)], where the maximum is taken over all positive integer solutions of the Diophantine equation rst=n(r+s+t).


0



1, 2, 3, 2, 3, 3, 3, 4, 4, 4, 4, 6, 3, 5, 5, 6, 4, 6, 5, 6, 7, 4, 5, 6, 5, 7, 9, 7, 6, 6, 5, 8, 9, 6, 8, 8, 3, 8, 9, 10, 7, 7, 5, 10, 9, 7, 7, 12, 7, 10, 9, 9, 7, 10, 11, 12, 9, 6, 7, 10, 7, 8, 11, 12, 13, 11, 5, 11, 9, 10, 9, 12, 5, 8, 15, 10, 12, 12, 9, 12, 12, 7, 8, 14, 15, 11, 11, 12, 10, 15
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OFFSET

1,2


COMMENTS

Conjecture: Max[t]=n(n+2) and Max[s]=2n, where the maxima are taken over all positive integer solutions r<=s<=t of the above Diophantine equation.


LINKS

Table of n, a(n) for n=1..90.


MATHEMATICA

(* Assuming given conjecture holds *) redu[n_] := Reap[ Do[ red = Reduce[0 < r <= s <= t && r*s*t == n*(r+s+t), r, Integers]; If[red =!= False, Sow[{r, s, t} /. ToRules[red] ] ], {s, 1, 2*n}, {t, s, n*(n+2)}] ][[2, 1]]; a[n_] := Max @@ Min @@@ redu[n]; a[1] = 1; Table[ Print[n, " ", an = a[n]]; an, {n, 1, 90}] (* JeanFrançois Alcover, Feb 22 2013 *)


CROSSREFS

Cf. A063520.
Sequence in context: A083060 A272979 A102351 * A248005 A129759 A137467
Adjacent sequences: A078170 A078171 A078172 * A078174 A078175 A078176


KEYWORD

nonn


AUTHOR

John W. Layman, Nov 20 2002


STATUS

approved



