A140863 - OEIS

%I #21 Dec 23 2018 11:39:03

%S 3,7,17,19,31,39,41,51,59,65,71,89,115,119,127,161,185,199,215,243,

%T 251,259,265,269,299,309,353,363,399,401,455,459,467,499,519,593,635,

%U 713,737,815,831,845,899,921,923,965,967,983,1011,1021,1025,1049,1053,1055

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

%C From _M. F. Hasler_ and _Farideh Firoozbakht_, Nov 26 2009: (Start)

%C The sequence of Mersenne primes, A000668 is a subsequence of this sequence.

%C 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)

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

%H Robert G. Wilson v, <a href="/A140863/b140863.txt">Table of n, a(n) for n = 1..579</a>

%H F. Firoozbakht, M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for Perfect Numbers</a>, JIS 13 (2010) #10.3.1.

%Y Cf. A000668. - _M. F. Hasler_ and _Farideh Firoozbakht_, Nov 26 2009

%Y Cf. A156903. - _Robert G. Wilson v_, Dec 09 2018

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Jul 20 2008

%E a(13)-a(54) from _Donovan Johnson_, Dec 09 2008