A291934 Largest k achievable by the iteration k->(sigma(k)+phi(k))/2 started at k=n, with termination when sigma(k) becomes odd.

1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, 16, 13, 16, 16, 16, 17, 18, 19, 25, 23, 23, 23, 36, 25, 29, 29, 36, 29, 53, 31, 32, 36, 36, 36, 36, 37, 53, 53, 53, 41, 144, 43, 61, 61, 47, 47, 144, 49, 50, 61, 61, 53, 144, 72, 72, 59, 59, 59, 107, 61, 144

Offset

1,2

Comments

See A291914 for types of termination. The first term with unknown conjecturally unbounded behavior is a(270). More values of n with this type of behavior are given in A291790.

All bounded terms of this sequence are either prime or in A028982.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..269

Hugo Pfoertner, Illustration of sequence terms for n<=5000, omitting n in A291790.

Example

a(38)=53: Starting with k=38 produces the trajectory 38 -> 39 -> 50 -> 53 -> 53 ...
a(42)=144: See example in A290001.

Mathematica

With[{lim = 100}, TakeWhile[#, # > 0 &] &@ Table[Which[Length@ # < lim, Last@ #, SameQ @@ Take[#, -2], Last@ #, True, 0] &@ NestWhileList[(DivisorSigma[1, #] + EulerPhi[#])/2 &, n, EvenQ@ DivisorSigma[1, #] &, 1, lim], {n, 270}]] (* Michael De Vlieger, Sep 06 2017 *)

Crossrefs

CF. A000010, A000040, A000203, A028982, A289997, A290001, A291789, A291790, A291791, A291914.

Sequence in context: A000015 A306369 A291784 * A291785 A364838 A122411

Adjacent sequences: A291931 A291932 A291933 * A291935 A291936 A291937

Keyword

nonn

Author

Hugo Pfoertner, Sep 06 2017

Status

approved