OFFSET
1,1
COMMENTS
From Robert Israel, Feb 01 2016: (Start)
Numbers k such that k^2 - 4*(d^2 + k^2/d^2) is a square for some divisor d of k.
All terms are divisible by 9.
MAPLE
filter:= proc(n) local x;
nops(select(x -> issqr(n^2-4*x^2 - 4*(n/x)^2), numtheory:-divisors(n)))>0;
end proc:
select(filter, [$1..10^6]); # Robert Israel, Feb 01 2016
MATHEMATICA
filterQ[n_] := Length@Select[Divisors[n], IntegerQ@Sqrt[n^2 - 4*#^2 - 4*(n/#)^2]&] > 0;
Select[Range[9, 999999, 9], filterQ] (* Jean-François Alcover, Jan 31 2023, after Robert Israel *)
PROG
(PARI) is(k) = fordiv(k, y, if(issquare(k^2 - 4*y^2 - 4*sqr(k/y)), return(1))); 0; \\ Jinyuan Wang, May 02 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Sep 24 2000
EXTENSIONS
a(19)-a(38) from Robert Israel, Feb 01 2016
New name from Jinyuan Wang, May 02 2021
STATUS
approved