Search: id:A007694
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%I A007694 M0992
%S A007694 1,2,4,6,8,12,16,18,24,32,36,48,54,64,72,96,108,128,144,162,
%T A007694 192,216,256,288,324,384,432,486,512,576,648,768,864,972,1024,1152,
%U A007694 1296,1458,1536,1728,1944,2048,2304,2592,2916,3072,3456,3888,4096
%N A007694 Numbers n such that phi(n) divides n.
%C A007694 a(n) divides p^a(n)-1 for all primes p>=5 - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Mar 22 2002
%C A007694 Also n such that sum( d divides n,mu(d)/d) has numerator=1 - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Apr 15 2002
%C A007694 n is here iff Phi[n] divides also Cototient[n]. On the other hand, Cototient[n] 
               divides Phi[n] iff n is a prime or power of prime. - Labos E. (labos(AT)ana.sote.hu), 
               May 03 2002
%D A007694 J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des 
               Nombres, Problem 526 pp. 71; 256, Ellipses Paris 2004.
%D A007694 Problem E3037, Amer. Math. Monthly 93 (1986), 656-657.
%D A007694 Sarkozy A. and Suranyi J., Number Theory Problem Book (in Hungarian), 
               Tankonyvkiado, Budapest, 1972.
%D A007694 W. Sierpinski, Elementary Theory of Numbers, Warsaw, 1964.
%D A007694 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007694 T. D. Noe, <a href="b007694.txt">Table of n, a(n) for n = 1..1000</a>
%H A007694 W. Sierpi\'{n}ski, <a href="http://matwbn.icm.edu.pl/kstresc.php?tom=42&wyd=10">
               Elementary Theory of Numbers</a>, Warszawa 1964.
%F A007694 n/EulerPhi(n) is integer iff n=1 or n=2^w*3^u for w=1, 2, ... and u=0, 
               1, 2, ...
%t A007694 Select[ Range[5000], IntegerQ[ #/EulerPhi[ # ]] &]
%Y A007694 Cf. A000010, A049237, A007694, A007947, A003557, A023200.
%Y A007694 Sequence in context: A067946 A145853 A064527 this_sequence A050622 A082662 
               A064522
%Y A007694 Adjacent sequences: A007691 A007692 A007693 this_sequence A007695 A007696 
               A007697
%K A007694 nonn,nice,easy
%O A007694 1,2
%A A007694 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

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