A110108 Conjectured values of n such that sigma(n)+sigma(k)=sigma(n+k) has no solution.

3, 9, 15, 21, 27, 39, 57, 63, 81, 93, 105, 117, 165, 171, 183, 189, 201, 219, 225, 243, 256, 279, 303, 309, 333, 351, 363, 375, 381, 387, 405, 417, 441, 453, 471, 489, 512, 543, 549, 567, 579, 603, 633, 651, 657, 669, 687, 693, 723, 729, 741, 777

Offset: 1

Author

T. D. Noe, Jul 12 2005

Keywords

• nonn

Comments

All k<10^10 have been checked. Note that this sequence appears to contain all powers of 3. It also contains 256 and 512, which are the only even numbers listed here.

All k<10^11 have been checked. 65 n values remain < 1000. - Donovan Johnson, Aug 29 2012

References

• R. K. Guy, Unsolved Problems in Number Theory, 3rd Ed., New York, Springer-Verlag, 2004, Section B15.

Crossrefs

Cf. A066435 (least k such that sigma(n)+sigma(k)=sigma(n+k)).

Extensions

Two terms removed (465 and 711) by Donovan Johnson, Aug 29 2012