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Search: id:A103291
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| A103291 |
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Numbers n such that sigma(2^n-1)>=2(2^n-1)-1, i.e., number 2^n-1 is perfect, abundant, or least deficient. |
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+0
4
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| 1, 12, 24, 36, 40, 48, 60, 72, 80, 84, 90, 96, 108, 120, 132, 140, 144, 156, 160, 168, 180, 192, 200, 204, 210, 216, 220, 228, 240, 252, 264, 270, 276, 280, 288, 300, 312, 320, 324, 330, 336, 348, 360, 372, 384, 396, 400, 408, 420, 432, 440, 444, 450, 456, 468
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Is there an odd number besides 1? Numbers 2^a(i)-1 form set difference of sequences A103289 and A096399.
Odd members > 1 exist, but there are none < 10^7. If n > 1 is an odd member, then 2^n-1 must have more than 900000 distinct prime factors, and all of them must be members of A014663. - David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
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FORMULA
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Such numbers n that 2^n-1 is in A103288.
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PROGRAM
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(PARI) for(i=1, 1000, n=2^i-1; if(sigma(n)>=2*n-1, print(i)));
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CROSSREFS
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Cf. A103288, A103289, A103292, A023196.
Adjacent sequences: A103288 A103289 A103290 this_sequence A103292 A103293 A103294
Sequence in context: A083547 A009185 A102308 this_sequence A103292 A059691 A097060
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KEYWORD
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hard,nonn
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AUTHOR
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Max Alekseyev (maxal(AT)cs.ucsd.edu), Jan 28 2005
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EXTENSIONS
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More terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
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