1,1

If 2^n-3 is prime (n is a term of A050414) then 2^(n-1)*(2^n-3) is in the sequence, this fact is a result of the following interesting theorem that I have found. Theorem: If k is an integer and 2^n-(2k+1) is prime then 2^(n-1)*(2^n-(2k+1)) is a solution of the equation sigma(x)=2(x+k). - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Feb 23 2005

Note that the fact " if 2^p-1 is prime then 2^(p-1)*(2^p-1) is a perfect number " is also a trivial result of this theorem. All known terms of this sequence are of the form 2^(n-1)*(2^n-3) where 2^n-3 is prime. Conjecture: There are no term of other forms. So likely next terms of this sequence are: 549754241024,8796086730752,140737463189504,144115187270549504, 2^93*(2^94-1),2^115*(2^116-1),2^121*(2^122-1),2^149*(2^150-1) and etc. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Feb 23 2005

Solutions to sigma[x]-2x=2

Abundances of terms in A045768: {-1,2,2,2,2,2,2,2,2,-1341930} so 1 and 1341931 are not here.

Cf. A045768.

Cf. A050414.

Sequence in context: A126859 A071334 A045768 this_sequence A063785 A135174 A109854

Adjacent sequences: A088828 A088829 A088830 this_sequence A088832 A088833 A088834

nonn

Labos E. (labos(AT)ana.sote.hu), Oct 28 2003

One more term from Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Feb 23 2005