A112645 Solutions to abs(sigma(x+1) - sigma(x)) = 2. Divisor sums of x and its neighbor x+1 differ from each other by 2.

1, 8, 26, 117, 2186, 145215, 1594322

Offset: 1

Author

Labos Elemer, Sep 28 2005

Keywords

• more
• nonn

Comments

Observe that form of 8, 26, 2186 and 1594322 is -1+3^j. Exponents of powers of 3 suitable as number n+1 are as follows: 2, 3, 7, 13, 71, 103. Is the next term 7509466514979724803946715958257546 = -1 + 3^71?

a(8) > 10^13. - Giovanni Resta, Jul 11 2013

Examples

			n = 1594322 = 2*797161 while n+1 = 3^13;
Sigma(n) = 2391486, sigma(n+1) = 2391484.
		

Crossrefs

Cf. A000203, A112646, A112647.

Programs

Mathematica

ta={{0}};Do[s=Abs[DivisorSigma[1, n+1]-DivisorSigma[1, n]]; If[Equal[s, 2], ta=Append[ta, n];Print[n]], {n, 1, 100000000}]; ta=Delete[ta, 1]