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%I #25 Nov 17 2015 09:46:07
%S 555,2691,9465,10017,16065,42693,64498,108717,164578,194990,204981,
%T 222794,488229,1696130,1705366,1824506,1838074,1981588,2079945,
%U 2125112,3823810,4112090,4292092,4956105,5354846,5848766,7462520,7597834,8394856
%N Numbers n such that sigma(n) = phi'(n), where sigma(n) is the sum of the divisors of n and phi'(n) is the arithmetic derivative of the Euler totient function of n.
%e phi(555) = 288 and 288' = 912 = sigma(555);
%e phi(2691) = 1584 and 1584' = 4368 = sigma(2691).
%p with(numtheory): P:=proc(q) local a,n,p; for n from 1 to q do
%p a:=phi(n)*add(op(2,p)/op(1,p),p=ifactors(phi(n))[2]);
%p if a=sigma(n) then print(n); fi; od; end: P(10^9);
%t d[1]=0; d[n_] := Total[n / Divide@@@ FactorInteger@ n]; Select[Range[10^5], DivisorSigma[1, #] == d@ EulerPhi@ # &] (* _Giovanni Resta_, Aug 21 2015 *)
%Y Cf. A000010, A000203, A003415.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Aug 18 2015