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 A110079 Numbers n such that sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n. 2
 5, 38, 284, 1370, 2168, 26828, 133088, 1515608, 19414448, 23521328, 25812848, 49353008, 82988756, 103575728, 537394688, 558504608, 921747488, 2651596448, 17517611968, 18249863488, 77792665408, 556915822208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Table of n, a(n) for n=1..22. MATHEMATICA Do[If[DivisorSigma[1, n] == 2n - 2^DivisorSigma[0, n], Print[n]], {n, 925000000}] CROSSREFS Cf. A110080-3. Sequence in context: A129048 A279489 A027323 * A110082 A073508 A282964 Adjacent sequences: A110076 A110077 A110078 * A110080 A110081 A110082 KEYWORD more,nonn AUTHOR Farideh Firoozbakht, Aug 03 2005 EXTENSIONS a(18)-a(21) from Donovan Johnson, Jan 31 2009 a(22) confirmed by Giovanni Resta, Aug 14 2013 STATUS approved

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Last modified February 21 15:08 EST 2024. Contains 370236 sequences. (Running on oeis4.)