A376641 - OEIS

%I #12 Oct 01 2024 11:52:53

%S 1,16,240,1680,23760,18480,498960,24386670,3991680,57805440,618068880,

%T 195093360,4944551040,1560746880,12485975040,99887800320,

%U 2696970608640,195093360000,1560746880000,5267520720000

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

%e a(1) = 16 =  2 * 2 * (2 + 2).

%e a(2) = 240 = 10 * 2 * (10 + 2)

%e            = 6 * 4 * (6 + 4).

%e a(3) = 1680 = 28 * 2 * (28 + 2)

%e             = 16 * 5 * (16 + 5)

%e             = 14 * 6 * (14 + 6).

%e a(4) = 23760 = 108 * 2 * (108 + 2)

%e            =  60 * 6 * (60 + 6)

%e            =  44 * 10 * (44 + 10)

%e            =  33 * 15 * (33 + 15).

%p N:= 10^8: # for terms <= N

%p V:= Vector(N,datatype=integer[1]):

%p for y from 2 to floor((N/2)^(1/3)) do

%p   for x from y do

%p     v:= x*y *(x+y);

%p     if v > N then break fi;

%p     V[v]:= V[v]+1

%p od od:

%p m:= max(V): R:= Array(0..m): count:= 0:

%p for i from 1 to N while count < m+1 do

%p   v:= V[i];

%p   if R[v] = 0 then R[v]:= i; count:= count+1 fi

%p od:

%p convert(R,list);

%Y Cf. A255265.

%K nonn,more

%O 0,2

%A _Robert Israel_, Sep 30 2024

%E a(12)-a(19) from _Chai Wah Wu_, Oct 01 2024