A067571 - OEIS

A067571

Numbers n such that determinant[{{n,phi(n)},{n+1,phi(n+1)}}]is a perfect square.

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

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

Det[{{26,phi(26)},{27,phi(27)}}] = Det[{{26,12},{27,18}}] = 12^2, so 26 is a term of the sequence.

MATHEMATICA

f[n_] := Det[{{n, EulerPhi[n]}, {n + 1, EulerPhi[n + 1]}}]; Do[If[IntegerQ @ Sqrt @ f[n], Print[n]], {n, 1, 10^5}]

PROG

(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

CROSSREFS

Cf. A000010, A067564, A067572.

Sequence in context: A072663 A276176 A050905 * A319486 A084298 A001772

Adjacent sequences: A067568 A067569 A067570 * A067572 A067573 A067574

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Jan 30 2002

EXTENSIONS

a(18)-a(37) from Amiram Eldar, Sep 26 2019

STATUS

approved