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%I #30 Apr 03 2023 10:36:10
%S 1,2,6,10,20,22,46,48,58,82,106,166,178,180,208,226,262,346,358,382,
%T 466,478,502,562,586,718,838,862,864,886,982,1018,1120,1186,1282,1306,
%U 1318,1366,1368,1438,1486,1522,1618,1822,1906,2026,2038,2062,2098,2206
%N Numbers n such that n = phi(phi(n) + sigma(n)).
%C If n=2*p where p is a Sophie Germain odd prime, then n is in the sequence; the proof is obvious.
%H K. D. Bajpai, <a href="/A097646/b097646.txt">Table of n, a(n) for n = 1..10000</a>
%H C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=SophieGermainPrime">Sophie Germain prime</a>.
%e 22 is in the sequence because phi(22)=10, sigma(22)=36 and phi(10+36)=22.
%p with(numtheory):K:=proc()local n,a,c; c:=1; for n from 1 to 5000000 do;
%p a:=phi(phi(n)+ sigma(n));if a=n then lprint(c,n); c:=c+1; fi;od; end:K(); # _K. D. Bajpai_, Jul 18 2013
%t Do[If[n==EulerPhi[EulerPhi[n]+DivisorSigma[1, n]], Print[n]], {n, 2400}]
%t Select[Range[2500],EulerPhi[EulerPhi[#]+DivisorSigma[1,#]]==#&] (* _Harvey P. Dale_, Jul 06 2021 *)
%o (PARI) is(n)=sigma(n=factor(n))==eulerphi(eulerphi(n)) \\ _Charles R Greathouse IV_, Nov 27 2013
%o (Magma) [n: n in [1..2300] | n eq EulerPhi(EulerPhi(n) + DivisorSigma(1,n))]; // _Vincenzo Librandi_, Aug 22 2015
%Y Cf. A097652, A005384, A097645, A018784.
%K nonn
%O 1,2
%A _Farideh Firoozbakht_, Sep 08 2004
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