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A057371 Numbers k that can be expressed as k = w+x = y*z with w*x = k*(y+z) where w, x, y, and z are all positive integers.

%I A057371 #19 May 04 2021 18:10:56
%S A057371 64,72,81,100,108,125,128,216,225,288,324,500,576,864,972,1125,1152,
%T A057371 1225,1800,2025,2700,3125,3200,3528,4500,7776,8100,10125,13068,13689,
%U A057371 15488,17496,18496,21125,24500,28800,34848,42336,44100,48672,55225,69696,93636,95256
%N A057371 Numbers k that can be expressed as k = w+x = y*z with w*x = k*(y+z) where w, x, y, and z are all positive integers.
%C A057371 All terms are powerful (A001694).
%e A057371 64 is a term because a solution exists at k=64, w=32, x=32, y=8, z=8:
%e A057371              k =  w + x  = y*z   with    w*x  =  k*(y+z)
%e A057371 becomes
%e A057371             64 = 32 + 32 = 8*8   with   32*32 = 64*(8+8).
%o A057371 (PARI) is(k) = fordiv(k, y, if(issquare(k^2 - 4*k*(y+k/y)), return(1))); 0; \\ _Jinyuan Wang_, May 01 2021
%Y A057371 Cf. A001694, A057369, A057370, A057372, A057373, A057421.
%K A057371 nonn
%O A057371 1,1
%A A057371 _Naohiro Nomoto_, Sep 23 2000
%E A057371 More terms from _Jinyuan Wang_, May 01 2021