

A173703


Composite numbers n with the property that phi(n) divides (n1)^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
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OFFSET

1,1


COMMENTS

All terms are odd because if n is even, (n1)^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. OllerMarcén, On kLehmer 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[(n1)^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 ( ( (n1)^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



