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

Author

Hugo Pfoertner, Sep 03 2017

Keywords

• nonn

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.

Examples

			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
		

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)

Crossrefs

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

Extensions

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