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A140863
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Odd numbers k such that sigma(m)=2m+k has a solution in m.(sigma is the sum-of-divisors function A000203).
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0
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3, 7, 17, 19, 31, 39, 41, 51, 59, 65, 71, 89, 115, 119, 127, 161, 185, 199, 215, 243, 251, 259, 265, 269, 299, 309, 353, 363, 399, 401, 455, 459, 467, 499, 519, 593, 635, 713, 737, 815, 831, 845, 899, 921, 923, 965, 967, 983, 1011, 1021, 1025, 1049, 1053, 1055
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Contribution from M. F. Hasler and F. Firoozbakht (mymontain(AT)yahoo.com), Nov 26 2009: (Start)
The sequence of Mersenne primes, A000668 is a subsequence of this sequence.
Because if k=2^p-1 is prime then n=2^(p-1)*(2^p-1)^2 is a solution of the
equation sigma(x)=2x+k. The proof is easy. (End)
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 196, pp 58, Ellipses, Paris 2008.
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CROSSREFS
| Cf. A000668. [From M. F. Hasler and F. Firoozbakht (mymontain(AT)yahoo.com), Nov 26 2009]
Sequence in context: A191147 A058887 A087749 * A076194 A167168 A064699
Adjacent sequences: A140860 A140861 A140862 * A140864 A140865 A140866
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 20 2008
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EXTENSIONS
| a(13)-a(54) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 09 2008
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