login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173703 Composite numbers n with the property that phi(n) divides (n-1)^2. 5
561, 1105, 1729, 2465, 6601, 8481, 12801, 15841, 16705, 19345, 22321, 30889, 41041, 46657, 50881, 52633, 71905, 75361, 88561, 93961, 115921, 126673, 162401, 172081, 193249, 247105, 334153, 340561, 378561, 449065, 460801, 574561, 656601, 658801, 670033 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are odd because if n is even, (n-1)^2 is odd and phi(n) is even for n > 2. - Donovan Johnson, Sep 08 2013

LINKS

Joerg Arndt and Donovan Johnson, Table of n, a(n) for n = 1..2000 (first 327 terms from Joerg Arndt)

José María Grau and Antonio M. Oller-Marcén, On k-Lehmer numbers, Integers, 12(2012), #A37

Nathan McNew, Radically weakening the Lehmer and Carmichael conditions (2012)

Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867v1 [math.NT], May 4, 2013.

EXAMPLE

a(1) = 561 is in the sequence because 560^2 = phi(561)*980 = 320*980 = 313600.

MATHEMATICA

Union[Table[If[PrimeQ[n] === False && IntegerQ[(n-1)^2/EulerPhi[n]], n], {n, 3, 100000}]]

PROG

(PARI)

N=10^9;

default(primelimit, N);

ct = 0;

{ for (n=4, N,

    if ( ! isprime(n),

        if ( ( (n-1)^2 % eulerphi(n) ) == 0,

            ct += 1;

            print(ct, " ", n);

        );

    );

); }

/* Joerg Arndt, Jun 23 2012 */

CROSSREFS

Cf. A000010, A207080.

Sequence in context: A104016 A002997 A087788 * A135720 A083733 A214428

Adjacent sequences:  A173700 A173701 A173702 * A173704 A173705 A173706

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Nov 25 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 26 16:10 EST 2014. Contains 250079 sequences.