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A068560 Numbers n such that phi(n)=tau(n)^2. 5
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; text; internal format)
OFFSET

1,2

COMMENTS

No more terms through 10^9. - Ryan Propper, 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, Apr 28 2011

LINKS

Table of n, a(n) for n=1..33.

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 *)

CROSSREFS

Cf. A039770.

Sequence in context: A213063 A268281 A223137 * A039773 A289947 A272955

Adjacent sequences:  A068557 A068558 A068559 * A068561 A068562 A068563

KEYWORD

easy,fini,nonn

AUTHOR

Benoit Cloitre, Mar 25 2002

EXTENSIONS

More terms from Ryan Propper, Jun 09 2006

STATUS

approved

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Last modified August 16 23:58 EDT 2018. Contains 313809 sequences. (Running on oeis4.)