A067135 Numbers k such that sigma(k+2) = 2*sigma(k-2).

5, 13, 313, 1153, 26206, 100318, 111928, 160873, 363283, 644278, 1676428, 2097808, 2639518, 3875998, 5349238, 5738773, 5903638, 6045583, 11272903, 13192933, 17242333, 18234403, 19667998, 29520643, 29595193, 31944238, 36918448, 37049803, 37201813, 43522288

Offset: 1

Author

Benoit Cloitre, Feb 18 2002

Keywords

• nonn

Comments

For each term given here except 5, k+2 is divisible by 3, but that is not always true: k = 149784995358 is a counterexample. Also, k+2 is divisible by 5 for all terms here except 5 and 26206, but it is also not true for k = 70333261.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..500 (first 80 terms from Vincenzo Librandi)

Crossrefs

Cf. A000203 (sigma), A067134.

Programs

Mathematica

Do[If[DivisorSigma[1, n+2] == 2*DivisorSigma[1, n-2], Print[n]], {n, 2, 10^9}] (* Ryan Propper, Sep 26 2005 *)

PARI

isok(k) = k > 2 && sigma(k+2) == 2*sigma(k-2); \\ Amiram Eldar, May 09 2025

Extensions

Edited by Dean Hickerson, Feb 20 2002

More terms from Ryan Propper, Sep 26 2005