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A007694
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Numbers n such that phi(n) divides n.
(Formerly M0992)
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14
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1, 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 162, 192, 216, 256, 288, 324, 384, 432, 486, 512, 576, 648, 768, 864, 972, 1024, 1152, 1296, 1458, 1536, 1728, 1944, 2048, 2304, 2592, 2916, 3072, 3456, 3888, 4096
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) divides p^a(n)-1 for all primes p>=5 - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 22 2002
Also n such that sum( d divides n,mu(d)/d) has numerator=1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 15 2002
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
It follows that n/phi(n) =2 if n is a power of 2 and =3 if n is of the form 6*A003586.[From Gary Detlefs, Jun 28 2011]
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REFERENCES
| J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 526 pp. 71; 256, Ellipses Paris 2004.
Problem E3037, Amer. Math. Monthly 93 (1986), 656-657.
Sarkozy A. and Suranyi J., Number Theory Problem Book (in Hungarian), Tankonyvkiado, Budapest, 1972.
W. Sierpinski, Elementary Theory of Numbers, Warsaw, 1964.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
W. Sierpi\'{n}ski, Elementary Theory of Numbers, Warszawa 1964.
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FORMULA
| n/EulerPhi(n) is integer iff n=1 or n=2^w*3^u for w=1, 2, ... and u=0, 1, 2, ...
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MATHEMATICA
| Select[ Range[5000], IntegerQ[ #/EulerPhi[ # ]] &]
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CROSSREFS
| Cf. A000010, A049237, A007694, A007947, A003557, A023200.
Cf. A003586
Sequence in context: A067946 A145853 A064527 * A050622 A082662 A064522
Adjacent sequences: A007691 A007692 A007693 * A007695 A007696 A007697
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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