cp's OEIS Frontend

A320538 Assuming the truth of the Collatz conjecture, a(n) is the number of divisors of n appearing in the Collatz trajectory of n.

%I A320538 #15 Apr 17 2020 07:22:19
%S A320538 1,2,2,3,2,4,2,4,2,4,2,6,2,4,3,5,2,4,2,6,2,4,2,8,3,4,2,6,2,6,2,6,3,4,
%T A320538 3,6,2,4,3,8,2,4,2,6,3,4,2,10,3,6,3,6,2,4,3,8,2,4,2,9,2,4,2,7,4,6,2,6,
%U A320538 2,6,2,8,2,4,2,6,3,6,2,10,2,4,2,6,2,4,2
%N A320538 Assuming the truth of the Collatz conjecture, a(n) is the number of divisors of n appearing in the Collatz trajectory of n.
%C A320538 a(p) = 2 for p prime.
%C A320538 a((2^2k - 1)/3) = 2, k = 1, 2, ...
%C A320538 We observe that a(n) differs from A093640(n) for n = 25, 27, 33, 35, 45, 49, 50, 54, 55, 57, 63, 65, 66, 70, 75, 77, 85, ...
%C A320538 7 occurs only eighteen times among the first 65537 terms. - _Antti Karttunen_, May 18 2019
%H A320538 Antti Karttunen, <a href="/A320538/b320538.txt">Table of n, a(n) for n = 1..65537</a>
%H A320538 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A320538 a(6) = 4 because the Collatz trajectory 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 contains 4 divisors of 6: 1, 2, 3 and 6.
%t A320538 lst={}; coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; Do[AppendTo[lst,Length[Intersection[Divisors[n],coll[n]]]],{n,1,100}]; lst
%o A320538 (PARI) f(n) = if(n%2, 3*n+1, n/2);
%o A320538 a(n) = {my(kn = n, nb = 1); while (n != 1, n = f(n); if ((kn % n) == 0, nb++);); nb;}
%Y A320538 Cf. A006370, A027750, A070165, A093640, A207674, A207675.
%K A320538 nonn
%O A320538 1,2
%A A320538 _Michel Lagneau_, Oct 15 2018