A260962 - OEIS

%I #18 Mar 11 2020 06:12:37

%S 8,26,122,351,31195,47201,51243,118265,300985,472491,672147,673863,

%T 850969,931383,1440625,3000927,3669213,3740755,4688645,4822143,

%U 4864175,11224565,13897079,13949343,16362857,16744355,18844265,19536205,35580099,38656975,42056215,46294105

%N Numbers k such that phi(k) = phi'(k'), where phi(k) is the Euler totient function of k and k' is the arithmetic derivative of k.

%H Amiram Eldar, <a href="/A260962/b260962.txt">Table of n, a(n) for n = 1..100</a>

%e Arithmetic derivative of 26 is 15, phi(15) = 8 and 8' = 12 that is equal to phi(26).

%p with(numtheory):P:=proc(q) local a,b,n,p;

%p for n from 1 to q do a:=phi(n*add(op(2,p)/op(1,p),p=ifactors(n)[2]));

%p b:=a*add(op(2,p)/op(1,p),p=ifactors(a)[2]);

%p if phi(n)=b then print(n); fi; od; end: P(10^9);

%t f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]; Select[Range@ 100000, f@ EulerPhi@ f@ # == EulerPhi@ # &] (* _Michael De Vlieger_, Aug 07 2015, after _Michael Somos_ at A003415 *)

%Y Cf. A000010, A003415, A190402, A260961.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Aug 06 2015