A110079 - OEIS

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

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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