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Numbers k such that sigma(phi(k)) - phi(k) = phi(sigma(k)), where phi(k) is the Euler totient function of k and sigma(k) is the sum of the divisors of k.
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%I #17 Jul 13 2019 12:15:30

%S 21,350,366,532,702,1072,5264,7128,23604,24102,30222,30636,32142,

%T 32274,34350,47338,70722,78530,113550,137214,197316,235624,292206,

%U 357490,367704,398346,406596,453096,453264,464820,479880,485460,504966,509124,512430,519870,539220

%N Numbers k such that sigma(phi(k)) - phi(k) = phi(sigma(k)), where phi(k) is the Euler totient function of k and sigma(k) is the sum of the divisors of k.

%H Amiram Eldar, <a href="/A271633/b271633.txt">Table of n, a(n) for n = 1..215</a> (terms below 10^9)

%e sigma(phi(21)) - phi(21) = 28 - 12 = 16 = phi(sigma(21)).

%p with(numtheory): P:= proc(q) local n; for n from 1 to q do

%p if sigma(phi(n))-phi(n)=phi(sigma(n)) then print(n); fi;

%p od; end: P(10^6);

%t Select[Range[10^6], DivisorSigma[1, #] - # &@ EulerPhi@ # == EulerPhi@ DivisorSigma[1, #] &] (* _Michael De Vlieger_, Apr 21 2016 *)

%o (PARI) isok(k) = my(x=eulerphi(k)); sigma(x) - x == eulerphi(sigma(k)); \\ _Michel Marcus_, Jul 13 2019

%Y Cf. A000010, A000203, A001065, A033632, A062401.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Apr 19 2016