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%I #24 Sep 03 2019 19:51:32
%S 45,694,3768374,6303735,15913725,20291271,42824146,47788894,54424095,
%T 141120134,163380694,219105494,305034794,404686557,790565966,
%U 893558445,928608435,1198745925,1251276254,1409720194,1412229015,1696122945
%N 1-sigma-balanced numbers: numbers n such that (sigma(n-d)+sigma(n+d))/2 = sigma(n) for d=1.
%C These terms, the 1-sigma-balanced numbers, seems to be significantly rarer than those with d=2,4,6,8,10.. It seems also that the 6-sigma-balanced numbers are very common.
%H Giovanni Resta, <a href="/A099632/b099632.txt">Table of n, a(n) for n = 1..91</a> (terms < 4*10^12)
%F Solutions to sigma(x-d)+sigma(x+d)=2*sigma(x) where d=1.
%e n=20291271, a=sigma(n-1)=37374480, b=sigma(n+1)=38104560, sigma(n)=37739520=(a+b)/2.
%t d=1;Do[s=(DivisorSigma[1, n+d]+DivisorSigma[1, n-d])/ 2-DivisorSigma[1, n];If[Equal[s, 0], Print[n]], {n, 1, 100000000}]
%o (PARI) is(n) = n>1 && (sigma(n-1)+sigma(n+1))/2==sigma(n) \\ _Felix Fröhlich_, Sep 03 2019
%Y Cf. A000203, A099631 (2-sigma-balanced numbers).
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 26 2004
%E a(10)-a(22) from _Donovan Johnson_, Feb 01 2009
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