A290144 Record lengths of transient part of the unitary aliquot sequences of the numbers in A290143.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 43, 45, 67, 78, 205, 207, 1109, 1116, 1117, 1155, 1162, 1163, 1171, 1711, 1712, 1828, 1829

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Example

The unitary aliquot sequence of 134 is: 134, 70, 74, 40, 14, 10, 8, 1. Its length is 8 and it is longer than the unitary aliquot sequences of all the numbers below 134.

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
g[n_] := If[n > 0, usigma[n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; a = 0; seq = {}; Do[b = Length[f[n]] - 2; If[b > a, a = b; AppendTo[seq, b]], {n, 10^6}]; seq (* after Giovanni Resta at A034448 & Robert G. Wilson v at A098009 *)

Crossrefs

Cf. A098008, A098009, A098010, A127652, A127653, A127654, A127655, A290143.

Sequence in context: A261293 A177872 A271839 * A115060 A004840 A254650

Adjacent sequences: A290141 A290142 A290143 * A290145 A290146 A290147

Keyword

nonn,more

Author

Amiram Eldar, Jul 21 2017

Status

approved