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A290001
Numbers k such that the iteration k -> (sigma(k)+phi(k))/2 terminates at a fraction later than at the first step.
8
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..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
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