%I #16 May 07 2024 07:04:41

%S 1,2,20,48,180,208,864,1120,1368,3552,58320,76416,79968,95488,107520,

%T 338688,570240,595968,653184,1347840,5199552,7918848,14592000,

%U 93699072,159138176,167078784,246688000,281640960,314548224,323985408,338411520,347578368,352002048

%N Numbers n such that n=phi(phi(n)+sigma(n)) and n is not of the form 2*p where p is a Sophie Germain odd prime.

%C It is obvious that if n=2*p where p is a Sophie Germain odd prime then n=phi(phi(n)+sigma(n)). This sequence is a subsequence of A097646. Except for the first term all terms of this sequence are even. There is no other term up to 3*10^7.

%H C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=SophieGermainPrime">Sophie Germain prime</a>.

%e 14592000 is in the sequence because 14592000=2*7296000, 7296000 is not a Sophie Germain odd prime and phi(phi(14592000)+sigma(14592000)) =14592000.

%t Do[If[(!PrimeQ[n/2]||!PrimeQ[n+1])&&n==EulerPhi[EulerPhi[n]+ DivisorSigma[1, n]], Print[n]], {n, 30000000}]

%Y Cf. A097646, A005384.

%K nonn

%O 1,2

%A _Farideh Firoozbakht_, Sep 09 2004

%E a(24)-a(33) from _Donovan Johnson_, Jan 18 2012