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A067571
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Numbers n such that determinant[{{n,phi(n)},{n+1,phi(n+1)}}]is a perfect square.
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0
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2, 26, 34, 68, 124, 160, 188, 342, 602, 776, 3104, 6324, 14688, 17170, 35894, 94500, 97094, 111036, 113102, 122180, 138096, 150314, 150624, 195396, 270106, 496706, 1035380, 1318064, 1428542, 1445120, 1968392, 2015720, 3149874, 3185300, 3774572, 4466898, 4970816
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OFFSET
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1,1
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COMMENTS
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If n is a term of the sequence, then the parallelogram formed by the vectors {n,phi(n)},{n+1,phi(n+1)} has the same area as that of an integral square.
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LINKS
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EXAMPLE
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Det[{{26,phi(26)},{27,phi(27)}}] = Det[{{26,12},{27,18}}] = 12^2, so 26 is a term of the sequence.
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MATHEMATICA
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f[n_] := Det[{{n, EulerPhi[n]}, {n + 1, EulerPhi[n + 1]}}]; Do[If[IntegerQ @ Sqrt @ f[n], Print[n]], {n, 1, 10^5}]
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PROG
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(PARI) isok(n) = issquare(matdet([n, eulerphi(n); n+1, eulerphi(n+1)])); \\ Michel Marcus, Sep 26 2019
(Magma) [k:k in [1..5000000]|IsSquare(k*EulerPhi(k+1)-(k+1)*EulerPhi(k))]; // Marius A. Burtea, Sep 26 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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