A146556 -id:A146556 - cp's OEIS frontend

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

Benoit Cloitre, Oct 02 2002

sign

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

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).

Cf. A146556, A005820, A069085, A113285.

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 *)

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

A215778 Natural growth of an aliquot sequence driven by a perfect number 2^(p-1)*((2^p)-1), but starting at 11.

Original entry on oeis.org

11, 13, 15, 33, 63, 145, 215, 313, 315, 933, 1563, 2613, 5003, 5005, 11123, 14869, 14871, 24793, 24795, 68805, 193275, 499885, 770627, 1152637, 1152639, 2216961, 4187619, 9032861, 9092323, 9272573, 9414403, 9414405, 37061115, 116692485, 351858171, 741077157, 1253259803

Offset: 1

V. Raman, Aug 23 2012

nonn

FactorDB, 369053696

Cf. A146556, A216224.

A216224 Natural growth of an aliquot sequence driven by a perfect number 2^(p-1)*((2^p)-1), but starting at 27.

Original entry on oeis.org

27, 53, 55, 89, 91, 133, 187, 245, 439, 441, 1041, 1743, 3633, 7503, 13329, 25203, 44429, 66547, 76813, 90803, 90805, 167243, 187957, 280907, 332005, 499739, 499741, 600995, 841405, 1177979, 1392181, 1977419, 1992661, 2398187, 3062293, 3600363, 6739253, 7507147

Offset: 1

Michel Marcus, Mar 13 2013

nonn

Quote from the abstract of the article by te Riele: "In this note, the existence of an aliquot sequence with more than 5092 monotonically increasing even terms is proved". The author uses the perfect number corresponding to the Mersenne prime 2^p-1 with p=19937 (whereas the script below only uses p=521).

H. J. J. te Riele, A note on the Catalan-Dickson conjecture, Math. Comp. 27 (1973), 189-192.

Cf. A146556, A215778.

lista(p=521, nb) = {perf = 2^(p-1)*(2^p-1); a = 27*perf; print1(a/perf, ", "); for (i=1, nb, a = sigma(a) - a; print1(a/perf, ", "); if (gcd(a/perf, p) != 1, return()););} \\ Michel Marcus, Mar 13 2013

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

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A215778 Natural growth of an aliquot sequence driven by a perfect number 2^(p-1)*((2^p)-1), but starting at 11.

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A216224 Natural growth of an aliquot sequence driven by a perfect number 2^(p-1)*((2^p)-1), but starting at 27.

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