login
Integers n such that -n is 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).
6

%I #16 Jul 14 2019 16:34:04

%S 4,10,11,12,18,19,20,22,25,28,29,30,31,32,36,39,40,42,43,44,48,50,51,

%T 52,54,56,58,59,61,67,69,70,72,76,78,84,85,86,88,89,91,92,95,96,100,

%U 101,102,103,104,105,107,108,109,112,113,115,116,120,122,123

%N Integers n such that -n is 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 Also numbers k such that A309144(k) > 0. - _Seiichi Manyama_, Jul 14 2019

%H Seiichi Manyama, <a href="/A102535/b102535.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="/A102535/a102535.txt">Solutions for 1 <= n <= 1000</a> (copy from MacLeod's website)

%Y Cf. A085514, A102778, A102779, A102809, A309144.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Mar 17 2005