OFFSET
1,3
COMMENTS
Taking any nonperfect number as initial value, does the map x->sigma(x)-2x lead to the cycle (-1,3,-2,7,-6,24,12,4) if during the iteration no perfect number is reached? Example: 124 -> -24 -> 108 -> 64 -> -1 -> 3 -> -2 -> 7 -> -6 -> 24 -> 12 -> 4 and the cycle (-1,3,-2,7,-6,24,12,4) is reached.
There appear to be lots of other cycles, for example the numbers in A005820 are cycles of length one. For longer cycles refer to the discussion in links. - Hans Havermann, Jul 21 2013
LINKS
Peter Luschny, Open questions posed in OEIS #1
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
Periodic with period (-1, 3, -2, 7, -6, 24, 12, 4) of length 8.
MATHEMATICA
NestList[DivisorSigma[1, #]-2#&, 1, 94] (* Peter Luschny, Jul 17 2013 *)
Join[{1}, LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {-1, 3, -2, 7, -6, 24, 12, 4}, 93]] (* Ray Chandler, Aug 25 2015 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Benoit Cloitre, Oct 02 2002
STATUS
approved