A207675 -id:A207675 - cp's OEIS frontend

A207674 Numbers such that all divisors occur in their Collatz trajectories.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 25, 26, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 86, 88, 89, 92, 94, 97, 98, 100, 101

Offset: 1

Reinhard Zumkeller, Feb 20 2012

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A027750, A070165, A006370, A207675 (complement), A000079 and A000040 are subsequences.

import Data.List (intersect)
a207674 n = a207674_list !! (n-1)
a207674_list = filter
   (\x -> a027750_row x `intersect` a070165_row x == a027750_row x) [1..]

coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; Select[Range[101],Complement[Divisors[#],coll[#]]=={}&] (* Jayanta Basu, May 27 2013 *)

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

Original entry on oeis.org

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, 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, 2, 6, 2, 8, 2, 4, 2, 6, 3, 6, 2, 10, 2, 4, 2, 6, 2, 4, 2

Offset: 1

Michel Lagneau, Oct 15 2018

nonn

a(p) = 2 for p prime.
a((2^2k - 1)/3) = 2, k = 1, 2, ...
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, ...
7 occurs only eighteen times among the first 65537 terms. - Antti Karttunen, May 18 2019

			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.

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A006370, A027750, A070165, A093640, A207674, A207675.

lst={}; coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]; Do[AppendTo[lst,Length[Intersection[Divisors[n],coll[n]]]],{n,1,100}]; lst

f(n) = if(n%2, 3*n+1, n/2);
a(n) = {my(kn = n, nb = 1); while (n != 1, n = f(n); if ((kn % n) == 0, nb++);); nb;}

cp's OEIS Frontend

A207674 Numbers such that all divisors occur in their Collatz trajectories.

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