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%I #26 Aug 18 2024 23:04:17
%S 1,4,646,1096,16174,22891,64672,353110,468970,515698,733570,1317343,
%T 1633213,1735288,2026945,2093506,2709542,4413772,5005825,5346241,
%U 5388154,6134527,12811666,15453229,19063174,20565214,22172791,35476021
%N Numbers k such that sigma(k+1)+sigma(k) = sigma(2k+1).
%C Integer solutions x to q=(sigma(x)+sigma(x+1))/sigma(x+x+1) such that q=1, i.e., sigma(x)+sigma(x+1)=sigma(2x+1); sigma()=A000203. - _Labos Elemer_, Feb 16 2004
%H Donovan Johnson, <a href="/A067171/b067171.txt">Table of n, a(n) for n = 1..100</a>
%t Do[s=(DivisorSigma[1, n]+DivisorSigma[1, n+1])/ DivisorSigma[1, 2*n+1];If[Equal[s, 1], Print[n]], {n, 1, 10000000}] (* _Labos Elemer_, Feb 16 2004 *)
%o (PARI) s1=1; for(n=1, 10^9, s2=sigma(n+1); if(s1+s2==sigma(2*n+1), print1(n, ", ")); s1=s2) /* _Donovan Johnson_, Sep 17 2013 */
%Y Cf. A000203, A091287, A091289, A091290.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Feb 18 2002
%E More terms from _Labos Elemer_, Feb 16 2004
%E Edited by _N. J. A. Sloane_, Oct 02 2008 at the suggestion of _R. J. Mathar_
%E a(22)-a(28) from _Donovan Johnson_, Jan 31 2009