OFFSET
0,3
LINKS
EXAMPLE
13, 14, 15 and 16 are in the sequence since 13 = 2^2 + 3^2, 14 = 1^2 + 2^2 + 3^2, 15 = (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2 and 16 = 4^2.
MAPLE
filter:= proc(n)
ormap(k -> issqr(-3*k^4+3*k^2+36*k*n) and ((3*k-3*k^2+sqrt(-3*k^4+3*k^2+36*k*n))/(6*k))::integer,
numtheory:-divisors(6*n))
end proc:
filter(0):= true:
select(filter, [$0..200]); # Robert Israel, Jan 22 2017
MATHEMATICA
filterQ[n_] := AnyTrue[Divisors[6n], IntegerQ[Sqrt[-3#^4 + 3#^2 + 36#*n]] && IntegerQ[(3# - 3#^2 + Sqrt[-3#^4 + 3#^2 + 36#*n])/(6#)]&];
filterQ[0] = True;
Select[Range[0, 200], filterQ] (* Jean-François Alcover, Feb 27 2019, after Robert Israel *)
PROG
(PARI) { isA062861(t) = fordiv(6*t, k, z=(k^2-1)/3; if(issquare(4*t/k-z), return(k)); if(z>4*t/k, break); ); 0 } \\ Max Alekseyev, Apr 26 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jun 25 2001
STATUS
approved