A068560 Numbers k such that phi(k) = tau(k)^2.

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

Offset

1,2

Comments

This sequence is finite because phi(k) >= sqrt(k) for all k >= 6, and for any e > 0, tau(k) < k^e for k large enough. Choosing e=1/4 gives tau(k)^2 < sqrt(k) <= phi(k). It remains unknown, however, if this sequence is full. - Nathaniel Johnston, Apr 28 2011

It can be shown that tau(k) <= 120 and the sequence is complete. - Max Alekseyev, May 30 2024

Links

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

Example

a(2) = A107655(2) = 5.

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, A068559, A107655, A114063.

Sequence in context: A213063 A268281 A223137 * A039773 A289947 A272955

Adjacent sequences: A068557 A068558 A068559 * A068561 A068562 A068563

Keyword

fini,full,nonn,changed

Author

Benoit Cloitre, Mar 25 2002

Extensions

More terms from Ryan Propper, Jun 09 2006

"full" keyword added by Max Alekseyev, May 30 2024

Status

approved