A114063 Numbers k such that phi(k) = tau(k)^4, where tau(k) = A000005(k).

1, 17, 514, 8738, 32301, 33003, 36351, 41504, 42292, 43852, 51860, 62226, 549117, 561051, 571311, 599067, 617967, 629811, 634005, 657495, 673184, 674505, 683168, 701024, 705568, 718964, 722684, 732628, 745484, 759772, 774368

Offset

1,2

Comments

For all large enough k, we have tau(k) < k^(1/5) and phi(k) > k^(4/5). Hence, tau(k)^4 < k^(4/5) < phi(k), implying that this sequence is finite. - Max Alekseyev, Mar 10 2016

Sequence is composed of 94030 terms. - Max Alekseyev, Jun 01 2024

Links

Max Alekseyev, Table of n, a(n) for n = 1..94030 (first 660 terms from Enrique Pérez Herrero; terms 661..7000 from Giovanni Resta)

Example

phi(33003) = 20736. tau(33003) = 12, 20736 = 12^4.
a(2) = A107655(4) = 17.

Mathematica

Select[Range[10^6], EulerPhi[#] == DivisorSigma[0, #]^4 &] (* Paolo Xausa, May 31 2024 *)

Prog

(PARI) isok(n) = eulerphi(n) == numdiv(n)^4; \\ Michel Marcus, Jan 22 2014

Crossrefs

Subsequence of A078164.

Cf. A020488, A062516, A063469, A063470, A107655, A112954, A112955, A175667, A068560, A068559.

Sequence in context: A185659 A012792 A012232 * A214135 A193120 A264858

Adjacent sequences: A114060 A114061 A114062 * A114064 A114065 A114066

Keyword

fini,full,nonn

Author

Giovanni Resta, Feb 13 2006

Status

approved