A110079 - OEIS

%I #9 Aug 14 2013 16:00:26

%S 5,38,284,1370,2168,26828,133088,1515608,19414448,23521328,25812848,

%T 49353008,82988756,103575728,537394688,558504608,921747488,2651596448,

%U 17517611968,18249863488,77792665408,556915822208

%N Numbers n such that sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n.

%C If 4^m+2^m-1 is prime then n=2^(m-1)*(4^m+2^m-1) is in the sequence because 2n-2^d(n)=2^m*(4^m+2^m-1)-2^(m*2)=2^m* (4^m-1)=2^m*(2^m-1)*(2^m+1)=(2^m-1)*(4^m+2^m)=sigma(2^(m-1)) *sigma(4^m+2^m-1)=sigma(2^(m-1)*(4^m+2^m-1))=sigma(n). A110082 gives such terms of this sequence.

%C a(22) <= 556915822208. a(23) <= 9311639470208. a(24) <= 29297682437888. - _Donovan Johnson_, Jan 31 2009

%C a(23) > 6*10^12. - _Giovanni Resta_, Aug 14 2013

%t Do[If[DivisorSigma[1, n] == 2n - 2^DivisorSigma[0, n], Print[n]], {n, 925000000}]

%Y Cf. A110080-3.

%K more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Aug 03 2005

%E a(18)-a(21) from _Donovan Johnson_, Jan 31 2009

%E a(22) confirmed by _Giovanni Resta_, Aug 14 2013