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 A306666 Positive integers x such that x*(7-5*x+x^2)*(6-4*x+x^2) is a square. 0
 1, 2, 3, 7, 21 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 29 17:22 EST 2023. Contains 367445 sequences. (Running on oeis4.)