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

1,1

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

Table of n, a(n) for n=1..38.

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

Prog

(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

Crossrefs

Cf. A146556, A215778.

Sequence in context: A044079 A044460 A160845 * A255364 A082915 A183032

Adjacent sequences: A216221 A216222 A216223 * A216225 A216226 A216227

Keyword

nonn

Author

Michel Marcus, Mar 13 2013

Status

approved