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A073407
Let phi_m(x) denote the Euler totient function applied m times to x. Sequence gives the minimum number of iterations m such that phi_m(n) divides n.
1
1, 1, 2, 1, 3, 1, 3, 1, 3, 2, 4, 1, 4, 2, 4, 1, 5, 1, 4, 2, 4, 3, 5, 1, 5, 3, 4, 2, 5, 3, 5, 1, 5, 4, 5, 1, 5, 3, 5, 2, 6, 3, 5, 3, 5, 4, 6, 1, 5, 4, 6, 3, 6, 1, 6, 2, 5, 4, 6, 3, 6, 4, 5, 1, 6, 4, 6, 4, 6, 4, 6, 1, 6, 4, 6, 3, 6, 4, 6, 2, 5, 5, 7, 3, 7, 4, 6, 3, 7, 4, 6, 4, 6, 5, 6, 1, 7, 4, 6, 4, 7, 5, 7, 3, 6
OFFSET
1,3
LINKS
FORMULA
It seems that sum(k=1, n, a(k)) is asymptotic to C*n*log(n) with C>1.
EXAMPLE
phi(22) -> 10, phi(10) -> 4, phi(4) -> 2 and 2 divides 22. Hence 3 iterations are needed and a(22) = 3.
MATHEMATICA
a[n_] := Module[{c = 0, k = n}, While[c == 0 || !Divisible[n, k], k = EulerPhi[k]; c++]; c]; Array[a, 105] (* Amiram Eldar, Jul 10 2019 *)
PROG
(PARI) a(n) = if(n<0, 0, c=1; s=n; while(n%eulerphi(s)>0, s=eulerphi(s); c++); c)
CROSSREFS
Sequence in context: A226859 A025820 A109704 * A049994 A135732 A342241
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 23 2002
STATUS
approved