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
McNew showed that the number of terms in this sequence below x is O(x^(6/7)). - Tomohiro Yamada, Sep 28 2020
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, International Journal of Number Theory 9 (2013), 1215-1224; available from arXiv, arXiv:1210.2001 [math.NT], 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.
MAPLE
isA173703 := proc(n)
n <> 1 and not isprime(n) and (modp( (n-1)^2, numtheory[phi](n)) = 0 );
end proc:
for n from 1 to 10000 do
if isA173703(n) then
printf("%d, \n", n);
end if;
end do: # R. J. Mathar, Nov 06 2017
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 *)
Select[Range[1, 700000, 2], CompositeQ[#]&&PowerMod[#-1, 2, EulerPhi[ #]] == 0&] (* Harvey P. Dale, Aug 10 2021 *)
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
KEYWORD
nonn
AUTHOR
José María Grau Ribas, Nov 25 2010
STATUS
approved