A075701 a(1)=1, a(n+1)=sigma(a(n))-2*a(n).

1, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6, 24, 12, 4, -1, 3, -2, 7, -6

Offset: 1

Author

Benoit Cloitre, Oct 02 2002

Keywords

• sign

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).

Crossrefs

Cf. A146556, A005820, A069085, A113285.

Programs

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 *)

Formula

Periodic with period (-1, 3, -2, 7, -6, 24, 12, 4) of length 8.