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%I #24 Apr 15 2019 07:23:20
%S 8,189,405,465,2187,2565,3483,6885,41283,46875,389691,796875,13410657,
%T 837134375,12557032155,23202024507,31335628125,38655885285,
%U 115964116965
%N Numbers n such that the arithmetic derivative of the cototient(n) is equal to the totient(n).
%C a(15) > 10^10. - _Amiram Eldar_, Jan 30 2019
%C 1.25*10^11 < a(20) <= 13421772796875. - _Giovanni Resta_, Apr 15 2019
%e (8 - phi(8))’ = (8 - 4)’ = 4’ = 4 = phi(8) ;
%e (189 - phi(189))’ = (189 - 108)’ = 81’ = 108 = phi(189).
%p with(numtheory): P:= proc(q) local n,p; for n from 1 to q do
%p if (n-phi(n))*add(op(2,p)/op(1,p),p=ifactors(n-phi(n))[2])=phi(n) then print(n);
%p fi; od; end: P(10^9);
%t Select[Range[10^6], Function[m, Function[k, If[Abs@ k < 2, 0, k Total[#2/#1 & @@@ FactorInteger[Abs@ k]]]][# - m] == m]@ EulerPhi@ # &] (* _Michael De Vlieger_, May 02 2016, after _Michael Somos_ at A003415 *)
%Y Cf. A000010, A003415, A051953, A272528.
%K nonn,more
%O 1,1
%A _Paolo P. Lava_, May 02 2016
%E a(14) from _Amiram Eldar_, Jan 30 2019
%E a(15)-a(19) from _Giovanni Resta_, Apr 15 2019
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