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A323077
Number of iterations of map x -> (x - (largest divisor d < x)) needed to reach 1 or a prime, when starting at x = n.
8
0, 0, 0, 1, 0, 1, 0, 2, 2, 1, 0, 2, 0, 1, 2, 3, 0, 3, 0, 2, 2, 1, 0, 3, 3, 1, 4, 2, 0, 3, 0, 4, 2, 1, 3, 4, 0, 1, 2, 3, 0, 3, 0, 2, 4, 1, 0, 4, 4, 4, 2, 2, 0, 5, 3, 3, 2, 1, 0, 4, 0, 1, 4, 5, 3, 3, 0, 2, 2, 4, 0, 5, 0, 1, 5, 2, 4, 3, 0, 4, 6, 1, 0, 4, 3, 1, 2, 3, 0, 5, 4, 2, 2, 1, 3, 5, 0, 5, 4, 5, 0, 3, 0, 3, 5
OFFSET
1,8
COMMENTS
When iteration is started from n, the first noncomposite reached is A006530(n), from which follows the new formula a(n) = A064097(A052126(n)) = A064097(n/A006530(n)), as A064097 is completely additive sequence. - Antti Karttunen, May 15 2020
FORMULA
If A001222(n) <= 1 [when n is 1 or a prime], a(n) = 0, otherwise a(n) = 1 + a(A060681(n)).
a(n) <= A064097(n).
a(n) = A064097(n) - A334202(n) = A064097(A052126(n)). - Antti Karttunen, May 13 2020
a(A334198(n)) = n for all n >= 0. - Antti Karttunen, May 19 2020
MATHEMATICA
Nest[Append[#1, If[PrimeOmega[#2] <= 1, 0, 1 + #1[[Max@ Differences@ Divisors[#2] ]] ]] & @@ {#, Length@ # + 1} &, {}, 105] (* Michael De Vlieger, May 26 2020 *)
PROG
(PARI)
A060681(n) = (n-if(1==n, n, n/vecmin(factor(n)[, 1])));
A323077(n) = if(1>=bigomega(n), 0, 1+A323077(A060681(n)));
CROSSREFS
Cf. A334198 (positions of the records, also the first occurrence of each n).
Differs from A334201 for the first time at n=169, where a(169) = 5, while A334201(169) = 6.
Sequence in context: A306863 A334108 A332813 * A334201 A257400 A328081
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 04 2019
STATUS
approved