A306666 Positive integers x such that x*(7-5*x+x^2)*(6-4*x+x^2) is a square.

1, 2, 3, 7, 21

Offset

1,2

Comments

No other terms below 10^6.

No other terms below 10^10. - Chai Wah Wu, Nov 24 2019

Links

Table of n, a(n) for n=1..5.

dxdy forum, x(7-5x+x^2)(6-4x+x^2)=y^2 in natural numbers (in Russian).

Mathematica

Select[Range[1000], IntegerQ[Sqrt[#*(7 - 5*# + #^2)*(6 - 4*# + #^2)]] &] (* Vaclav Kotesovec, Mar 10 2019 *)

Prog

(PARI) isok(x)=issquare(x*(7-5*x+x^2)*(6-4*x+x^2));
(Python)
from sympy.ntheory.primetest import is_square
A306666_list = [n for n in range(1, 10**3) if is_square(n*(n*(n*(n*(n - 9) + 33) - 58) + 42))] # Chai Wah Wu, Nov 24 2019

Crossrefs

Sequence in context: A222890 A011968 A080021 * A032313 A032223 A002863

Adjacent sequences: A306663 A306664 A306665 * A306667 A306668 A306669

Keyword

nonn,more

Author

Dmitry Ezhov, Mar 04 2019

Status

approved