A290001 Numbers k such that the iteration k -> (sigma(k)+phi(k))/2 terminates at a fraction later than at the first step.

12, 14, 15, 20, 24, 28, 33, 34, 35, 42, 48, 54, 55, 56, 62, 63, 69, 70, 76, 77, 78, 84, 85, 86, 87, 88, 90, 93, 94, 95, 96, 99, 102, 104, 105, 108, 110, 111, 112, 118, 119, 120, 122, 123, 124, 125, 129, 130, 132, 141, 142, 143, 148, 150

Offset

1,1

Comments

Termination at the first step occurs if k>3 is a square or twice a square, i.e. if k is a term of A028982. So the sequence lists the numbers that end at a fraction but are not of one of these two forms.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..101

Hugo Pfoertner, Table of n, a(n) for n = 1..1136 (values above first 101 terms are only guesses)

N. J. A. Sloane, Iterating some number-theoretic functions, Posting to Seqfan mailing list, Sep 3, 2017

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Example

42 is in the sequence because the following iteration reaches an odd sigma(k):
   k        sigma(k)     phi(k)
   42          96          12  k->(sigma(k)+phi(k))/2, (96+12)/2=54
   54         120          18  k->(sigma(k)+phi(k))/2, (120+18)/2=69
   69          96          44  ...
   70         144          24  ...
   84         224          24
  124         224          60
  142         216          70
  143         168         120  k->(sigma(k)+phi(k))/2, (168+120)/2=144
  144         403          48  sigma(144) is odd, iteration terminates

Crossrefs

Cf. A000010, A000203, A028982, A289997, A291790, A291791.

Sequence in context: A355148 A344980 A344883 * A371422 A080693 A135739

Adjacent sequences: A289998 A289999 A290000 * A290002 A290003 A290004

Keyword

nonn

Author

Hugo Pfoertner, Sep 03 2017

Extensions

b-file curtailed beyond last certain value, moved other values to a-file. - N. J. A. Sloane, Oct 01 2017

Status

approved