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A376641 a(n) is the first positive integer that has exactly n representations as x * y * (x + y) where x >= y > 1.

%I A376641 #12 Oct 01 2024 11:52:53
%S A376641 1,16,240,1680,23760,18480,498960,24386670,3991680,57805440,618068880,
%T A376641 195093360,4944551040,1560746880,12485975040,99887800320,
%U A376641 2696970608640,195093360000,1560746880000,5267520720000
%N A376641 a(n) is the first positive integer that has exactly n representations as x * y * (x + y) where x >= y > 1.
%e A376641 a(1) = 16 =  2 * 2 * (2 + 2).
%e A376641 a(2) = 240 = 10 * 2 * (10 + 2)
%e A376641            = 6 * 4 * (6 + 4).
%e A376641 a(3) = 1680 = 28 * 2 * (28 + 2)
%e A376641             = 16 * 5 * (16 + 5)
%e A376641             = 14 * 6 * (14 + 6).
%e A376641 a(4) = 23760 = 108 * 2 * (108 + 2)
%e A376641            =  60 * 6 * (60 + 6)
%e A376641            =  44 * 10 * (44 + 10)
%e A376641            =  33 * 15 * (33 + 15).
%p A376641 N:= 10^8: # for terms <= N
%p A376641 V:= Vector(N,datatype=integer[1]):
%p A376641 for y from 2 to floor((N/2)^(1/3)) do
%p A376641   for x from y do
%p A376641     v:= x*y *(x+y);
%p A376641     if v > N then break fi;
%p A376641     V[v]:= V[v]+1
%p A376641 od od:
%p A376641 m:= max(V): R:= Array(0..m): count:= 0:
%p A376641 for i from 1 to N while count < m+1 do
%p A376641   v:= V[i];
%p A376641   if R[v] = 0 then R[v]:= i; count:= count+1 fi
%p A376641 od:
%p A376641 convert(R,list);
%Y A376641 Cf. A255265.
%K A376641 nonn,more
%O A376641 0,2
%A A376641 _Robert Israel_, Sep 30 2024
%E A376641 a(12)-a(19) from _Chai Wah Wu_, Oct 01 2024