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A320538 Assuming the truth of the Collatz conjecture, a(n) is the number of divisors of n appearing in the Collatz trajectory of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to 3x+1 (or Collatz) problem

EXAMPLE

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.

MATHEMATICA

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

PROG

(PARI) 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; }

CROSSREFS

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

Sequence in context: A157986 A025479 A093640 * A343650 A327391 A083903

Adjacent sequences:  A320535 A320536 A320537 * A320539 A320540 A320541

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 15 2018

STATUS

approved

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Last modified October 16 06:47 EDT 2021. Contains 348040 sequences. (Running on oeis4.)