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A068560
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Numbers n such that phi(n)=tau(n)^2.
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3
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1, 5, 34, 63, 76, 128, 136, 170, 315, 364, 380, 444, 640, 680, 972, 1820, 1824, 1836, 2142, 2220, 4788, 4860, 6000, 8064, 8568, 8736, 9120, 9180, 10710, 23940, 40320, 42840, 43680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| No more terms through 10^9. - Ryan Propper (rpropper(AT)stanford.edu), Jun 09 2006
This sequence is finite because phi(n) >= sqrt(n) for all n >= 6, and for any e>0, tau(n) < n^e for n large enough. Choosing e=1/4 gives tau(n)^2 < sqrt(n) <= phi(n). It remains unknown, however, if this sequence is full. - Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 28 2011
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MATHEMATICA
| Do[If[EulerPhi[n] == DivisorSigma[0, n]^2, Print[n]], {n, 10^5}] (* Ryan Propper, Jun 09 2006 *)
Select[Range[10^5], EulerPhi[#] == DivisorSigma[0, #]^2 &] (* Alonso del Arte, Aug 25 2011 *)
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CROSSREFS
| Cf. A039770.
Sequence in context: A145505 A193325 A124936 * A039773 A135973 A186636
Adjacent sequences: A068557 A068558 A068559 * A068561 A068562 A068563
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KEYWORD
| easy,fini,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 25 2002
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Jun 09 2006
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