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

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

Author

Michel Marcus, Mar 13 2013

Keywords

• nonn

Comments

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).

Links

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

Crossrefs

Cf. A146556, A215778.

Programs

PARI

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