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A140863 Odd numbers k such that sigma(m) = 2m+k has a solution in m, where sigma is the sum-of-divisors function A000203. 2
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; text; internal format)
OFFSET

1,1

COMMENTS

From M. F. Hasler and Farideh Firoozbakht, 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)

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 196, p. 58, Ellipses, Paris 2008.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..579

F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.

CROSSREFS

Cf. A000668. - M. F. Hasler and Farideh Firoozbakht, Nov 26 2009

Cf. A156903. - Robert G. Wilson v, Dec 09 2018

Sequence in context: A058887 A306355 A087749 * A076194 A167168 A064699

Adjacent sequences:  A140860 A140861 A140862 * A140864 A140865 A140866

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Jul 20 2008

EXTENSIONS

a(13)-a(54) from Donovan Johnson, Dec 09 2008

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)