A099631 -id:A099631 - cp's OEIS frontend

A099632 1-sigma-balanced numbers: numbers n such that (sigma(n-d)+sigma(n+d))/2 = sigma(n) for d=1.

45, 694, 3768374, 6303735, 15913725, 20291271, 42824146, 47788894, 54424095, 141120134, 163380694, 219105494, 305034794, 404686557, 790565966, 893558445, 928608435, 1198745925, 1251276254, 1409720194, 1412229015, 1696122945

Offset: 1

Labos Elemer, Oct 26 2004

nonn

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.

			n=20291271, a=sigma(n-1)=37374480, b=sigma(n+1)=38104560, sigma(n)=37739520=(a+b)/2.

Giovanni Resta, Table of n, a(n) for n = 1..91 (terms < 4*10^12)

Cf. A000203, A099631 (2-sigma-balanced numbers).

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}]

is(n) = n>1 && (sigma(n-1)+sigma(n+1))/2==sigma(n) \\ Felix Fröhlich, Sep 03 2019

Solutions to sigma(x-d)+sigma(x+d)=2*sigma(x) where d=1.

a(10)-a(22) from Donovan Johnson, Feb 01 2009

A099633 Numbers k such that (phi(k-2) + phi(k+2))/2 = phi(k); 2-phi/balanced numbers.

Original entry on oeis.org

5, 10, 14, 20, 25, 50, 80, 154, 200, 434, 520, 610, 815, 1205, 1345, 2680, 3200, 3560, 4669, 7330, 9290, 10130, 11705, 17630, 24410, 25090, 33385, 34205, 39754, 39785, 40870, 48470, 55979, 59090, 73165, 75470, 78035, 95990, 107680, 115685, 120230

Offset: 1

Labos Elemer, Oct 27 2004

nonn

			k=154, phi(152)=72, phi(156)=48, phi(154)=60.

Donovan Johnson, Table of n, a(n) for n = 1..499

Cf. A066167, A000010, A099631, A099632.

Flatten[Position[Partition[EulerPhi[Range[121000]],5,1],?((#[[1]]+ #[[5]]) /2 == #[[3]]&),{1},Heads->False]]+2 (* _Harvey P. Dale, Jan 20 2015 *)

isok(k) = (k>2) && (eulerphi(k-2)+eulerphi(k+2) == 2*eulerphi(k)); \\ Michel Marcus, Nov 18 2022

Incorrect term 2 removed by Michel Marcus, Nov 19 2022

cp's OEIS Frontend

A099632 1-sigma-balanced numbers: numbers n such that (sigma(n-d)+sigma(n+d))/2 = sigma(n) for d=1.

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