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A173703 Composite numbers n with the property that phi(n) divides (n-1)^2. 6
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}]]

Select[Range[700000], CompositeQ[#]&&Divisible[(#-1)^2, EulerPhi[#]]&] (* Harvey P. Dale, Nov 29 2014 *)

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 A263403 A083733

Adjacent sequences:  A173700 A173701 A173702 * A173704 A173705 A173706

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Nov 25 2010

STATUS

approved

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Last modified December 9 13:48 EST 2016. Contains 278971 sequences.