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A270807 Trajectory of 1 under the map n -> n + n/gpf(n) + 1 (see A269304).

%I A270807 #24 Apr 06 2016 13:16:54
%S A270807 1,3,5,7,9,13,15,19,21,25,31,33,37,39,43,45,55,61,63,73,75,91,99,109,
%T A270807 111,115,121,133,141,145,151,153,163,165,181,183,187,199,201,205,211,
%U A270807 213,217,225,271,273,295,301,309,313,315,361,381,385,421,423,433,435,451,463,465
%N A270807 Trajectory of 1 under the map n -> n + n/gpf(n) + 1 (see A269304).
%C A270807 _Cody M. Haderlie_ (see A269304) conjectures that the trajectory of any initial value will eventually merge with this sequence. The trajectory of 2, for example, begins 2, 4, 7, 9, 13, 15, 19, 21, 25, ... and from 7 on coincides with this sequence. See A271418.
%H A270807 Chai Wah Wu, <a href="/A270807/b270807.txt">Table of n, a(n) for n = 1..10000</a>
%o A270807 (Python)
%o A270807 from __future__ import division
%o A270807 from sympy import primefactors
%o A270807 A270807_list, b = [], 1
%o A270807 for i in range(10000):
%o A270807     A270807_list.append(b)
%o A270807     b += b//(max(primefactors(b)+[1])) + 1 # _Chai Wah Wu_, Apr 06 2016
%o A270807 (PARI) gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
%o A270807 lista(nn) = {a = 1; for (n=1, nn, print1(a, ", "); a = a + a/gpf(a) + 1;);} \\ _Michel Marcus_, Apr 06 2016
%Y A270807 Cf. A006530, A269304, A271418.
%Y A270807 For first differences see A270808.
%K A270807 nonn
%O A270807 1,2
%A A270807 _N. J. A. Sloane_, Apr 05 2016