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A130776 Numbers n such that the sum of the proper divisors of n and n+1 equals either n or n+1. 0

%I

%S 1,2,3,4,6,7,16,28,31,38,127,256,278,469,1298,3477,7298,7525,8191,

%T 13969,19909,26738,31492,65536,99381,131071,357698,524287,20742482,

%U 33550336,772499089,1959272066

%N Numbers n such that the sum of the proper divisors of n and n+1 equals either n or n+1.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AliquotDivisor.html">Aliquot Divisor./</a>.

%e 16 has the proper divisors 1,2,4 and 8. 17 has the proper divisor 1. The sum of those divisors is 16, therefore 16 is in the sequence.

%t Select[Range[1000000], DivisorSigma[1, # ] + DivisorSigma[1, # + 1] - 2*# - 1 == # || DivisorSigma[1, # ] + DivisorSigma[1, # + 1] - 2*# - 1 == # + 1 &]

%t lst = {}; d1 = d2 = 1; Do[ d2 = DivisorSigma[1, n + 1]; d = d1 + d2 - 2 n - 1; If[d == n || d == n + 1, Print@n; AppendTo[lst, n]]; d1 = d2, {n, 2*10^9}]; lst (* _Robert G. Wilson v_ *)

%K nonn

%O 1,2

%A _J. M. Bergot_, Jul 14 2007

%E Edited, corrected and extended by _Stefan Steinerberger_, Jul 16 2007

%E a(29) - a(32) from _Robert G. Wilson v_, Jul 27 2007

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)