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A066782 Numbers n such that (n, phi(n)) lies on the hyperbola x^2 - y^2 = m^2, for some natural number m, i.e., n^2 - phi(n)^2 = m^2. 1
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 (list; graph; refs; listen; history; text; internal format)
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) { n=0; for (m=1, 10^10, if (issquare(m^2 - eulerphi(m)^2), write("b066782.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 25 2010

CROSSREFS

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

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Last modified December 2 18:41 EST 2021. Contains 349445 sequences. (Running on oeis4.)