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A260962 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.

%I A260962 #18 Mar 11 2020 06:12:37
%S A260962 8,26,122,351,31195,47201,51243,118265,300985,472491,672147,673863,
%T A260962 850969,931383,1440625,3000927,3669213,3740755,4688645,4822143,
%U A260962 4864175,11224565,13897079,13949343,16362857,16744355,18844265,19536205,35580099,38656975,42056215,46294105
%N A260962 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 A260962 Amiram Eldar, <a href="/A260962/b260962.txt">Table of n, a(n) for n = 1..100</a>
%e A260962 Arithmetic derivative of 26 is 15, phi(15) = 8 and 8' = 12 that is equal to phi(26).
%p A260962 with(numtheory):P:=proc(q) local a,b,n,p;
%p A260962 for n from 1 to q do a:=phi(n*add(op(2,p)/op(1,p),p=ifactors(n)[2]));
%p A260962 b:=a*add(op(2,p)/op(1,p),p=ifactors(a)[2]);
%p A260962 if phi(n)=b then print(n); fi; od; end: P(10^9);
%t A260962 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 A260962 Cf. A000010, A003415, A190402, A260961.
%K A260962 nonn,easy
%O A260962 1,1
%A A260962 _Paolo P. Lava_, Aug 06 2015