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%I #26 Jan 11 2022 05:51:05
%S 1,9,10,11,14,15,18,26,29,30,31,34,35,37,38,42,43,44,48,52,53,54,55,
%T 57,59,62,63,64,67,69,70,71,73,74,75,76,82,84,85,86,90,92,93,94,95,96,
%U 98,100,101,102,103,105,106,108,111,112,116,117,122,125,126,127,128
%N Integers n representable as the product of the sum of three nonzero integers with the sum of their reciprocals: n=(x+y+z)*(1/x+1/y+1/z).
%C See under A086446 for comments and references.
%H Seiichi Manyama, <a href="/A085514/b085514.txt">Table of n, a(n) for n = 1..1000</a>
%H A. Bremner, R. K. Guy and R. Nowakowski, <a href="https://doi.org/10.1090/S0025-5718-1993-1189516-5">Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?</a>, Math. Comp. 61 (1993) 117-130.
%H Allan J. MacLeod, <a href="http://web.archive.org/web/20100125135648/http://maths.paisley.ac.uk/allanm/ECRNT/knight/knintro.htm">Knight's Problem</a>
%H Allan J. MacLeod, <a href="/A085514/a085514.txt">Solutions for 11 <= n <= 999</a> (copy from MacLeod's website)
%H Nguyen Xuan Tho, <a href="https://doi.org/10.33039/ami.2021.04.005">What positive integers n can be presented in the form n = (x + y + z)(1/x + 1/y + 1/z)?</a>, Annales Mathematicae et Informaticae 54 (2021).
%e a(1)=1 because (1+1-1)*(1/1+1/1-1/1)=1.
%e a(2)=(1+1+1)*(1/1+1/1+1/1)=9.
%e a(9)=(2-15+78)*(1/2-1/15+1/78)=29.
%Y Cf. A086446 (representation by positive x, y, z), A102535 (representable negative n)
%Y See A102774, A102775, A102777 for values of x, y, z corresponding to values of n >= 11.
%K nonn
%O 1,2
%A _Hugo Pfoertner_, Jul 19 2003
%E Corrected and extended by _David J. Rusin_, Jul 30 2003
%E More terms from the MacLeod web site, Mar 17 2005
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