A066782 Numbers k such that (k, phi(k)) lies on the hyperbola x^2 - y^2 = m^2, for some natural number m, i.e., k^2 - phi(k)^2 is a square.

1, 5, 13, 25, 34, 41, 61, 68, 113, 125, 136, 169, 181, 219, 222, 272, 313, 390, 421, 444, 482, 544, 578, 613, 625, 657, 666, 761, 780, 888, 964, 979, 1013, 1088, 1156, 1170, 1201, 1301, 1332, 1560, 1681, 1741, 1776, 1861

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

5^2 - phi(5)^2 = 25 - 16 = 3^2, so 5 is a term of the sequence.

Mathematica

Select[ Range[ 1, 10^4 ], IntegerQ[ Sqrt[ #^2 - EulerPhi[ # ]^2 ] ] & ]

Prog

(PARI) isok(k) = { issquare(k^2 - eulerphi(k)^2) } \\ Harry J. Smith, Mar 25 2010

Crossrefs

Cf. A066763.

Sequence in context: A190618 A309585 A004627 * A094553 A094079 A194811

Adjacent sequences: A066779 A066780 A066781 * A066783 A066784 A066785

Keyword

nonn

Author

Joseph L. Pe, Jan 18 2002

Status

approved