%I A075398
%S A075398 4,8,32,128,8192,131072,524288,2147483648,2305843009213693952,618970019642690137449562112,
%T A075398 162259276829213363391578010288128,170141183460469231731687303715884105728
%N A075398 Perfect powers pp such that pp-1 is prime.
%C A075398 If n is in the sequence then n is a solution of the equation sigma(sigma(x)-x)=x 
               (*). Because if 2^p-1 is prime and n=2^p then sigma(sigma(n)-n)=sigma((2^(p+1)-1)-2^p)=sigma(2^p-1)=2^p=n\
               . Is it true that there is no other solution for (*)? - Farideh Firoozbakht 
               (mymontain(AT)yahoo.com), Dec 05 2005
%C A075398 Twice even superperfect numbers (cf. A061652). Also twice superperfect 
               numbers, if there are no odd superperfect numbers (cf. A019279). 
               Difference between n-th ultraperfect number and n-th infraperfect 
               number. - Omar E. Pol (info(AT)polprimos.com), Apr 25 2008
%H A075398 O. E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica 
               de los numeros primos y perfectos"</a>.
%F A075398 a(n) = 2^A000043(n). - Omar E. Pol (info(AT)polprimos.com), Apr 11 2008
%F A075398 a(n) = A139306(n) - A139096(n). a(n) = 2*A061652(n). Also a(n) = 2*A019279(n) 
               if there are no odd superperfect numbers. - Omar E. Pol (info(AT)polprimos.com), 
               Apr 25 2008
%F A075398 A075398(n)=(1+Sqrt[1+8*A000396(n)])/2 [From Artur Jasinski (grafix(AT)csl.pl), 
               Sep 23 2008]
%Y A075398 Equals Mersenne primes (A000668) + 1.
%Y A075398 Cf. A000043.
%Y A075398 Cf. A019279, A061652, A129096, A129306.
%Y A075398 Sequence in context: A113479 A103970 A034785 this_sequence A072868 A098579 
               A032467
%Y A075398 Adjacent sequences: A075395 A075396 A075397 this_sequence A075399 A075400 
               A075401
%K A075398 easy,nonn
%O A075398 1,1
%A A075398 Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002