OFFSET
1,1
COMMENTS
a(n) is the first positive number that can be represented in exactly n ways as 3*x*(x^2+2*y^2) = (x-y)^3 + x^3 + (x+y)^3 for positive numbers x and y.
Note that the first term x-y of the arithmetic progression need not be positive.
From Ondrej Kutal, Dec 21 2022: (Start)
a(14) <= 41605309793862144.
a(15) <= 35049191875384896000.
a(16) <= 25550860877155589184000. (End)
EXAMPLE
a(3) = 792 because 792 = (-6)^3 + 2^3 + 10^3 = (-1)^3 + 4^3 + 9^3 = 4^3 + 6^3 + 8^3 is the first number that can be represented in exactly 3 ways.
MAPLE
N:= 5*10^10:
L:= NULL:
for a from 1 while 3*a^3 <= N do
for b from 1 do
x:= 3*a*(a^2 + 2*b^2);
if x > N then break fi;
L:= L, x
od od:
L:= sort([L]):
V:= Vector(11):
m:= L[1]: count:= 1:
for i from 2 to nops(L) do
if L[i] = m then count:= count+1
else
if V[count] = 0 then V[count]:= m fi;
count:= 1; m:= L[i];
fi
od:
convert(V, list);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Dec 15 2022
EXTENSIONS
a(12)-a(13) from Ondrej Kutal, Dec 21 2022
STATUS
approved