OFFSET
1,3
COMMENTS
Squares that are not in this sequence are 49, 169, 196, 361, 441, 676, ...
This is the list of squares not of the form A050931(k)^2. A number n is in this sequence iff n = m^2 with m having no prime factor == 1 (mod 6). - M. F. Hasler, Mar 04 2018
FORMULA
a(n) = A230780(n-1)^2 for n > 1.
EXAMPLE
Loeschian number 25 = 5^2 is a term because 25 = x^2 + x*y + y^2 has no solution for positive integers x, y.
MAPLE
isA024614:= proc(n) local x, y;
for x from 1 to floor(sqrt(n-1)) do
if issqr(4*n-3*x^2) then return true fi
od:
false
end proc:
isA024614(0):= false:
remove(isA024614, [seq(i^2, i=0..200)]); # Robert Israel, Mar 02 2018
MATHEMATICA
sol[s_] := Solve[0 < x <= y && s == x^2 + x y + y^2, {x, y}, Integers];
Select[Range[0, 100]^2, sol[#] == {}&] (* Jean-François Alcover, Oct 26 2020 *)
PROG
(PARI) is(n, m)=issquare(n, m)&&!setsearch(Set(factor(m)[, 1]%6), 1) \\ second part is equivalent to is_A230780(m), this is sufficient to test (e.g., to produce a list) if we know that n = m^2. - M. F. Hasler, Mar 04 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Mar 02 2018
STATUS
approved