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

1, 16, 240, 1680, 23760, 18480, 498960, 24386670, 3991680, 57805440, 618068880, 195093360, 4944551040, 1560746880, 12485975040, 99887800320, 2696970608640, 195093360000, 1560746880000, 5267520720000

Offset: 0

Author

Robert Israel, Sep 30 2024

Keywords

• nonn
• more

Examples

			a(1) = 16 =  2 * 2 * (2 + 2).
a(2) = 240 = 10 * 2 * (10 + 2)
           = 6 * 4 * (6 + 4).
a(3) = 1680 = 28 * 2 * (28 + 2)
            = 16 * 5 * (16 + 5)
            = 14 * 6 * (14 + 6).
a(4) = 23760 = 108 * 2 * (108 + 2)
           =  60 * 6 * (60 + 6)
           =  44 * 10 * (44 + 10)
           =  33 * 15 * (33 + 15).
		

Crossrefs

Cf. A255265.

Programs

Maple

N:= 10^8: # for terms <= N
V:= Vector(N,datatype=integer[1]):
for y from 2 to floor((N/2)^(1/3)) do
  for x from y do
    v:= x*y *(x+y);
    if v > N then break fi;
    V[v]:= V[v]+1
od od:
m:= max(V): R:= Array(0..m): count:= 0:
for i from 1 to N while count < m+1 do
  v:= V[i];
  if R[v] = 0 then R[v]:= i; count:= count+1 fi
od:
convert(R,list);

Extensions

a(12)-a(19) from Chai Wah Wu, Oct 01 2024