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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. 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 *) 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 * A300629 A135720 A263403 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 March 17 08:45 EDT 2018. Contains 300557 sequences. (Running on oeis4.)