1,1

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

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

O. E. Pol, Determinacion geometrica de los numeros primos y perfectos".

a(n) = 2^A000043(n). - Omar E. Pol (info(AT)polprimos.com), Apr 11 2008

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

A075398(n)=(1+Sqrt[1+8*A000396(n)])/2 [From Artur Jasinski (grafix(AT)csl.pl), Sep 23 2008]

Equals Mersenne primes (A000668) + 1.

Cf. A000043.

Cf. A019279, A061652, A129096, A129306.

Sequence in context: A113479 A103970 A034785 this_sequence A072868 A098579 A032467

Adjacent sequences: A075395 A075396 A075397 this_sequence A075399 A075400 A075401

easy,nonn

Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002