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

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

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: A355656 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