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%I #27 Mar 02 2019 01:58:25
%S 36,40,48,72,80,90,96,108,120,126,144,160,168,176,180,192,200,216,225,
%T 234,240,252,270,280,288,297,300,320,324,336,352,360,378,384,396,400,
%U 405,408,420,432,440,448,450,456,468,480
%N Numbers n expressible as a product of 4 factors in two different ways, n = a*b*c*d = x*y*w*z, with a+b+c+d = x+y+w+z.
%C The first few terms have a+b+c+d = w+x+y+z equal to 14, 15, 12, 15, 16, 17, 15, ..., . - _Robert G. Wilson v_, Feb 09 2015
%H Robert G. Wilson v, <a href="/A254836/b254836.txt">Table of n, a(n) for n = 1..1114</a> (first 157 terms from Carmine Suriano)
%e 40 is in the list since 40 = 1*1*5*8 = 1*2*2*10 and 1+1+5+8 = 15 = 1+2+2+10.
%t fQ[n_] := If[ PrimeOmega@ n > 3, Block[{k = 1}, While[k < n && Length@ Select[ IntegerPartitions[k, {4}, Divisors@ n], Times @@ # == n &] < 2, k++]; If[k < 2n, True]]]; k = 1; lst = {}; While[k < 500, If[ fQ@ k, AppendTo[lst, k]]; k++]; lst (* _Robert G. Wilson v_, Feb 09 2015 *)
%Y Cf. A060292.
%K nonn
%O 1,1
%A _Carmine Suriano_, Feb 08 2015
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