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URL: https://oeis.org/A053475

⇱ A053475 - OEIS

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A053475
1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n.
11
2, 3, 3, 4, 3, 5, 3, 5, 4, 6, 3, 6, 3, 6, 4, 6, 3, 7, 3, 7, 5, 7, 3, 7, 4, 7, 5, 7, 3, 8, 3, 7, 4, 8, 4, 8, 3, 8, 5, 8, 3, 9, 3, 8, 6, 8, 3, 8, 4, 9, 4, 8, 3, 9, 5, 8, 6, 9, 3, 9, 3, 8, 6, 8, 4, 9, 3, 9, 5, 9, 3, 9, 3, 9, 5, 9, 4, 10, 3, 9, 6, 10, 3, 10, 6, 9, 4, 9, 3, 10, 4, 9, 5, 9, 4, 9, 3, 9, 6, 10, 3, 10
OFFSET
1,1
COMMENTS
Analogous sequences of iteration-lengths for A000005 or A000010 are A036459 and A049108 resp. The length values of 3 occur if the initial value is prime resulting in {p,1,0} iterations.
FORMULA
a(n) = A076640(n) + 1. - Michael De Vlieger, Jul 04 2016
EXAMPLE
Starting with n=18, the iterations of A051953 are as follows: {18,12,8,4,2,1,0}. The length of this sequence is 7, so a(18) = 7. The function is applied a(n)-1 times.
MATHEMATICA
Table[Length@ NestWhileList[# - EulerPhi@ # &, n, # > 0 &], {n, 84}] (* Michael De Vlieger, Jul 04 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 14 2000
STATUS
approved