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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
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
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.)