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A053475
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1 + the number of iterations of A051953 (Euler-cototient) function needed to reach 0, starting at n (n is counted).
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11
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| Smallest number of steps j such that Nest[cototient, n, j]=0, where cototient[n] = n - EulerPhi[n]
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EXAMPLE
| Starting with n=100, the iterations of A051953 are as follows: {100,60,44,24,16,8,4,2,1,0}. The length of this sequence generated by 100 is a[n]= a[100]. The function is applied a[n]-1 times
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CROSSREFS
| A000005, A000010, A051953, A036459, A049108.
Sequence in context: A086925 A088858 A113312 * A140605 A049878 A038203
Adjacent sequences: A053472 A053473 A053474 * A053476 A053477 A053478
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jan 14 2000
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