The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A173743

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A173743

Numbers k such that phi(tau(k)) = tau(rad(k)).
(history; published version)

#14 by Charles R Greathouse IV at Thu Sep 08 08:45:50 EDT 2022

PROG

(MAGMAMagma) [ k:k in [1..360]| EulerPhi(#Divisors(k)) eq #Divisors(&*PrimeDivisors(k)) ]; // Marius A. Burtea, Jul 09 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#13 by Alois P. Heinz at Tue Jul 09 11:11:18 EDT 2019

STATUS

editing

approved

#12 by Alois P. Heinz at Tue Jul 09 11:11:02 EDT 2019

NAME

Numbers k such that phi(tau(k)) = tau(rad(k)).

FORMULA

{ n : A163109(n) = A034444(n)) }.

STATUS

proposed

editing

#11 by Marius A. Burtea at Tue Jul 09 09:10:33 EDT 2019

STATUS

editing

proposed

#10 by Marius A. Burtea at Tue Jul 09 09:08:37 EDT 2019

PROG

(MAGMA) [ k:k in [1..360]| EulerPhi(#Divisors(k)) eq #Divisors(&*PrimeDivisors(k)) ]; // Marius A. Burtea, Jul 09 2019

STATUS

proposed

editing

#9 by Michel Marcus at Tue Jul 09 08:24:10 EDT 2019

STATUS

editing

proposed

#8 by Michel Marcus at Tue Jul 09 08:24:07 EDT 2019

LINKS

Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler's_phi_function"> Euler's totient function</a>

EXTENSIONS

Added punctuation to the examples - R. J. Mathar, Mar 05 2010

STATUS

proposed

editing

#7 by Amiram Eldar at Tue Jul 09 07:09:07 EDT 2019

STATUS

editing

proposed

#6 by Amiram Eldar at Tue Jul 09 07:08:35 EDT 2019

MATHEMATICA

rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[360], EulerPhi[ DivisorSigma[0, #] ] == DivisorSigma[0, rad[#]] &] (* Amiram Eldar, Jul 09 2019 *)

#5 by Amiram Eldar at Tue Jul 09 07:08:14 EDT 2019

NAME

Numbers n k such that phi(tau(nk))= tau(rad(nk)) .

LINKS

Amiram Eldar, <a href="/A173743/b173743.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[360], EulerPhi[ DivisorSigma[0, #] ] == DivisorSigma[0, rad[#]] &] (* Amiram Eldar, Jul 09 2019*)

CROSSREFS

Cf. A000010, A000005, A007947, A034444, A163109.

STATUS

approved

editing