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Numbers k such that sigma(k+1) = 2*sigma(k).
8

%I #27 Dec 09 2024 23:23:22

%S 5,125,1253,1673,3127,5191,7615,12035,43817,47795,48559,49955,56975,

%T 58373,61721,63545,68033,78395,97411,106001,108473,109939,111451,

%U 111683,123497,123797,131659,137081,192065,192279,224561,228377,274273,280313,290417,290719,351815

%N Numbers k such that sigma(k+1) = 2*sigma(k).

%C Sequence seems to consist only of odd values.

%H Harry J. Smith, <a href="/A067081/b067081.txt">Table of n, a(n) for n = 1..761</a>

%t f[n_]:=DivisorSigma[1,n]; lst={};Do[If[2*f[n]==f[n+1],AppendTo[lst,n]],{n,9!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 22 2009 *)

%t Position[Partition[DivisorSigma[1,Range[300000]],2,1],_?(2#[[1]]==#[[2]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Oct 21 2024 *)

%o (PARI) isok(k) = { sigma(k+1) == 2*sigma(k) } \\ _Harry J. Smith_, May 08 2010

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 18 2002

%E Terms added by _Harry J. Smith_, May 08 2010