|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|