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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.
0
1, 16, 240, 1680, 23760, 18480, 498960, 24386670, 3991680, 57805440, 618068880, 195093360, 4944551040, 1560746880, 12485975040, 99887800320, 2696970608640, 195093360000, 1560746880000, 5267520720000
OFFSET
0,2
EXAMPLE
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).
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);
CROSSREFS
Cf. A255265.
Sequence in context: A264343 A283411 A161591 * A227440 A103975 A162791
KEYWORD
nonn,more
AUTHOR
Robert Israel, Sep 30 2024
EXTENSIONS
a(12)-a(19) from Chai Wah Wu, Oct 01 2024
STATUS
approved