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

Author

Labos Elemer, Oct 26 2004

Keywords

• nonn

Comments

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.

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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}]

PARI

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

Formula

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

Extensions

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