A110079 Numbers n such that sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n.

5, 38, 284, 1370, 2168, 26828, 133088, 1515608, 19414448, 23521328, 25812848, 49353008, 82988756, 103575728, 537394688, 558504608, 921747488, 2651596448, 17517611968, 18249863488, 77792665408, 556915822208

Offset: 1

Author

Farideh Firoozbakht, Aug 03 2005

Keywords

• more
• nonn

Comments

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.

a(22) <= 556915822208. a(23) <= 9311639470208. a(24) <= 29297682437888. - Donovan Johnson, Jan 31 2009

a(23) > 6*10^12. - Giovanni Resta, Aug 14 2013

Crossrefs

Cf. A110080-3.

Programs

Mathematica

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

Extensions

a(18)-a(21) from Donovan Johnson, Jan 31 2009

a(22) confirmed by Giovanni Resta, Aug 14 2013